qu.1.topic=1-elementary functions@ qu.1.1.mode=Formula@ qu.1.1.comment=The answer is \${mathml("\$answer")}.@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$J=range(2,9); \$N=range(2,9); \$H=range(0,5); \$C=range(0,5); \$D=range(1,6); \$B=range(-8,8,2); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1),0)); \$rR=rint(7); \$R=switch(rint(7),"1/2","1/4","3/4","1/5","2/5","3/5","4/5"); \$BR=\$B*\$R; \$RM=\$R-1; \$rP=rint(3); \$P=switch(\$rP,\$B*\$X^("\$R"),\$B*\$X^(-\$J),\$B*sqrt(\$X)); \$PP=switch(\$rP,\$BR*\$X^(\$RM),-\$B*\$J*\$X^(-\$J-1),(\$B/2)/sqrt(\$X)); \$rS=rint(3); \$S=switch(\$rS,\$C*sin(\$A*\$X),\$C*cos(\$A*\$X),\$C*tan(\$A*\$X)); \$SP=switch(\$rS,\$C*\$A*cos(\$A*\$X),-\$C*\$A*sin(\$A*\$X),\$C*\$A*(sec(\$A*\$X))^2); \$rU=rint(3); \$U=switch(\$rU,\$D*"e"^(\$K*\$X),\$D*ln(\$N*\$X),\$N^\$X); \$UP=switch(\$rU,\$D*\$K*"e"^(\$K*\$X),\$D/\$X,"ln(\$N)"*\$N^\$X); \$rFa=rint(4); \$rFb=rint(4); \$rFc=rint(4); \$rFd=rint(4); condition:not(eq(\$rFa,\$rFb)); condition:not(eq(\$rFc,\$rFd)); condition:not(eq((\$rFa-\$rFc)*(\$rFb-\$rFc),0)); condition:not(eq((\$rFa-\$rFd)*(\$rFb-\$rFd),0)); \$Fa=switch(\$rFa,"\$P",\$S,"\$U",\$H); \$FPa=switch(\$rFa,\$PP,\$SP,"\$UP",0); \$Fb=switch(\$rFb,"\$P",\$S,"\$U",\$H); \$FPb=switch(\$rFb,\$PP,\$SP,"\$UP",0); \$Fc=switch(\$rFc,"\$P",\$S,"\$U",\$H); \$FPc=switch(\$rFc,\$PP,\$SP,"\$UP",0); \$Fd=switch(\$rFd,"\$P",\$S,"\$U",\$H); \$FPd=switch(\$rFd,\$PP,\$SP,"\$UP",0); \$function="\$Fa+\$Fb+\$Fc+\$Fd"; \$answer="\$FPa+\$FPb+\$FPc+\$FPd";@ qu.1.1.question=Find the derivative of \${mathml("\$function")}.@ qu.1.1.answer=\$answer@ qu.1.2.mode=Formula@ qu.1.2.comment=The answer is \${mathml("\$answer")}.@ qu.1.2.editing=useHTML@ qu.1.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$J=range(2,9); \$N=range(2,9); \$H=range(0,5); \$C=range(0,5); \$D=range(1,6); \$B=range(-8,8,2); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1),0)); \$rR=rint(7); \$R=switch(rint(7),"1/2","1/4","3/4","1/5","2/5","3/5","4/5"); \$BR=\$B*\$R; \$RM=\$R-1; \$rP=rint(3); \$P=switch(\$rP,\$B*\$X^("\$R"),\$B*\$X^(-\$J),\$B*sqrt(\$X)); \$PP=switch(\$rP,\$BR*\$X^(\$RM),-\$B*\$J*\$X^(-\$J-1),(\$B/2)/sqrt(\$X)); \$rT=rint(2); \$T=switch(\$rT,\$C*arcsin(\$X),\$C*arctan(\$X)); \$TP=if(eq(\$C,0),0,switch(\$rT,\$C/sqrt(1-\$X^2),\$C/(1+\$X^2))); \$rU=rint(3); \$U=switch(\$rU,\$D*"e"^(\$K*\$X),\$D*ln(\$N*\$X),\$N^\$X); \$UP=switch(\$rU,\$D*\$K*"e"^(\$K*\$X),\$D/\$X,"ln(\$N)"*\$N^\$X); \$rFa=rint(4); \$rFb=rint(4); \$rFc=rint(4); \$rFd=rint(4); condition:not(eq(\$rFa,\$rFb)); condition:not(eq(\$rFc,\$rFd)); condition:not(eq((\$rFa-\$rFc)*(\$rFb-\$rFc),0)); condition:not(eq((\$rFa-\$rFd)*(\$rFb-\$rFd),0)); \$Fa=switch(\$rFa,"\$P",\$T,"\$U",\$H); \$FPa=switch(\$rFa,\$PP,\$TP,"\$UP",0); \$Fb=switch(\$rFb,"\$P",\$T,"\$U",\$H); \$FPb=switch(\$rFb,\$PP,\$TP,"\$UP",0); \$Fc=switch(\$rFc,"\$P",\$T,"\$U",\$H); \$FPc=switch(\$rFc,\$PP,\$TP,"\$UP",0); \$Fd=switch(\$rFd,"\$P",\$T,"\$U",\$H); \$FPd=switch(\$rFd,\$PP,\$TP,"\$UP",0); \$function="\$Fa+\$Fb+\$Fc+\$Fd"; \$answer="\$FPa+\$FPb+\$FPc+\$FPd";@ qu.1.2.question=Find the derivative of \${mathml("\$function")}.@ qu.1.2.answer=\$answer@ qu.2.topic=2-products@ qu.2.1.mode=Formula@ qu.2.1.comment=The answer is \${mathml("\$answer")}.@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$AP=range(2,8); \$AQ=range(2,8,2);\$BP=range(-9,9); \$BQ=range(-9,9); \$BT=range(-9,9); \$CP=range(2,8); \$CT=range(2,8); \$J=range(2,8); \$K=range(-6,6); condition:not(eq(\$BP*\$BQ*\$BT*\$K*(\$K-1),0)); \$N=range(2,8); \$NM=\$N-1; \$rP=rint(3); \$P=switch(\$rP,\$AP*\$X^\$N+\$BP,\$AP*\$X^\$N+\$BP*\$X,\$AP*\$X^2+\$BP*\$X+\$CP); \$PP=switch(\$rP,\$AP*\$N*\$X^(\$NM),(\$AP*\$N*\$X^(\$NM)+\$BP),(2*\$AP*\$X+\$BP)); \$rQ=rint(3); \$Q=switch(\$rQ,\$AQ*sqrt(\$X)+\$BQ,\$AQ*\$X^(-\$J)+\$BQ,\$AQ*\$X^(-\$J)+\$BQ*\$X); \$QP=switch(\$rQ,(\$AQ/2)/sqrt(\$X),-\$AQ*\$J*\$X^(-\$J-1),-\$AQ*\$J*\$X^(-\$J-1)+\$BQ); \$rT=rint(3); \$T=switch(\$rT,"e"^(-\$CT*\$X),"e"^(-\$CT*\$X)+\$BT,"e"^(\$K*\$X)+\$BT*\$X); \$TP=switch(\$rT,-\$CT*"\$T",-\$CT*"e"^(-\$CT*\$X),(\$K*"e"^(\$K*\$X)+\$BT)); \$r=rint(4); \$F=switch(\$r,\$P,\$Q,\$P,\$Q); \$FP=switch(\$r,\$PP,\$QP,\$PP,\$QP); \$G=switch(\$r,\$Q,\$P,"\$T","\$T"); \$GP=switch(\$r,\$QP,\$PP,"\$TP","\$TP"); \$function=(\$F)*("\$G"); \$answer=(\$FP)*("\$G")+(\$F)*("\$GP");@ qu.2.1.question=Find the derivative of \${mathml("\$function")}.@ qu.2.1.answer=\$answer@ qu.2.2.mode=Formula@ qu.2.2.comment=The answer is \${mathml("\$answer")}.@ qu.2.2.editing=useHTML@ qu.2.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$AP=range(2,8); \$AQ=range(2,8,2); \$AS=range(2,8); \$BP=range(-9,9); \$BQ=range(-9,9); \$BT=range(-9,9); \$CP=range(2,8); \$CT=range(2,8); \$J=range(2,8); \$K=range(-6,6); condition:not(eq(\$BP*\$BQ*\$BT*\$K*(\$K-1),0)); \$N=range(2,8); \$NM=\$N-1; \$rP=rint(3); \$P=switch(\$rP,\$AP*\$X^\$N+\$BP,\$AP*\$X^\$N+\$BP*\$X,\$AP*\$X^2+\$BP*\$X+\$CP); \$PP=switch(\$rP,\$AP*\$N*\$X^(\$NM),(\$AP*\$N*\$X^(\$NM)+\$BP),(2*\$AP*\$X+\$BP)); \$rQ=rint(3); \$Q=switch(\$rQ,\$AQ*sqrt(\$X)+\$BQ,\$AQ*\$X^(-\$J)+\$BQ,\$AQ*\$X^(-\$J)+\$BQ*\$X); \$QP=switch(\$rQ,(\$AQ/2)/sqrt(\$X),-\$AQ*\$J*\$X^(-\$J-1),-\$AQ*\$J*\$X^(-\$J-1)+\$BQ);\$rT=rint(3); \$T=switch(\$rT,"e"^(-\$CT*\$X),"e"^(-\$CT*\$X)+\$BT,"e"^(\$K*\$X)+\$BT*\$X); \$TP=switch(\$rT,-\$CT*"\$T",-\$CT*"e"^(-\$CT*\$X),(\$K*"e"^(\$K*\$X)+\$BT)); \$rS=rint(3); \$S=switch(\$rS,sin(\$AS*\$X),cos(\$AS*\$X),tan(\$AS*\$X)); \$SPf=switch(\$rS,cos(\$AS*\$X),sin(\$AS*\$X),(sec(\$AS*\$X))^2); \$SPc=switch(\$rS,\$AS,-\$AS,\$AS); \$rT=rint(3); \$rF=rint(3); \$F=switch(\$rF,\$P,\$Q,"\$T"); \$FP=switch(\$rF,\$PP,\$QP,"\$TP"); \$function=("\$F")*(\$S); \$answer=("\$FP")*(\$S)+\$SPc*("\$F")*(\$SPf);@ qu.2.2.question=Find the derivative of \${mathml("\$function")}.@ qu.2.2.answer=\$answer@ qu.3.topic=3-quotients@ qu.3.1.mode=Formula@ qu.3.1.comment=The answer is \${mathml("\$answer")}.@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$AP=range(2,9); \$AQ=range(2,9); \$BP=range(-9,9); \$BQ=range(-9,9); \$BT=range(-9,9); \$CP=range(2,6); \$CQ=range(2,6); \$CT=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$BP*\$BQ*\$BT,0)); \$NP=range(2,6); \$NPM=\$NP-1; \$NQ=range(2,6); \$NQM=\$NQ-1; \$rP=rint(3); \$rQ=rint(3); condition:not(eq(\$rP,\$rQ)); \$P=switch(\$rP,\$AP*\$X^\$NP+\$BP,\$AP*\$X^\$NP+\$BP*\$X,\$AP*\$X^2+\$BP*\$X+\$CP); \$PP=switch(\$rP,\$AP*\$NP*\$X^(\$NPM),(\$AP*\$NP*\$X^(\$NPM)+\$BP),(2*\$AP*\$X+\$BP)); \$Q=switch(\$rQ,\$AQ*\$X^\$NQ+\$BQ,\$AQ*\$X^\$NQ+\$BQ*\$X,\$AQ*\$X^2+\$BQ*\$X+\$CQ); \$QP=switch(\$rQ,\$AQ*\$NQ*\$X^(\$NQM),(\$AQ*\$NQ*\$X^(\$NQM)+\$BQ),(2*\$AQ*\$X+\$BQ)); \$rT=rint(2); \$T=switch(\$rT,\$CT*"e"^(\$K*\$X)+\$BT,\$CT*"e"^(\$K*\$X)+\$BT*\$X); \$TP=switch(\$rT,\$CT*\$K*"e"^(\$K*\$X),(\$CT*\$K*"e"^(\$K*\$X)+\$BT)); \$r=rint(3); \$F=switch(\$r,\$P,"\$T",\$P); \$FP=switch(\$r,\$PP,"\$TP",\$PP); \$G=switch(\$r,\$Q,\$Q,"\$T"); \$GP=switch(\$r,\$QP,\$QP,"\$TP"); \$function="\$F"/"\$G"; \$num=if(lt(2*\$rQ+\$r,2),("\$FP")*(\$G)-\$GP*("\$F"),"(\$FP)*(\$G)-(\$F)*(\$GP)"); \$answer="(\$num)/(\$G)^2";@ qu.3.1.question=Find the derivative of \${mathml("\$function")}.@ qu.3.1.answer=\$answer@ qu.3.2.mode=Formula@ qu.3.2.comment=The answer is \${mathml("\$answer")}.@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$AP=range(2,9); \$AQ=range(2,9); \$AS=range(2,9); \$BP=range(-9,9); \$BQ=range(-9,9); \$BT=range(-9,9); \$CP=range(2,6); \$CQ=range(2,6); \$CT=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$BP*\$BQ*\$BT,0)); \$NP=range(2,6); \$NPM=\$NP-1; \$NQ=range(2,6); \$NQM=\$NQ-1; \$rP=rint(3); \$rQ=rint(3); condition:not(eq(\$rP,\$rQ)); \$P=switch(\$rP,\$AP*\$X^\$NP+\$BP,\$AP*\$X^\$NP+\$BP*\$X,\$AP*\$X^2+\$BP*\$X+\$CP); \$PP=switch(\$rP,\$AP*\$NP*\$X^(\$NPM),(\$AP*\$NP*\$X^(\$NPM)+\$BP),(2*\$AP*\$X+\$BP)); \$Q=switch(\$rQ,\$AQ*\$X^\$NQ+\$BQ,\$AQ*\$X^\$NQ+\$BQ*\$X,\$AQ*\$X^2+\$BQ*\$X+\$CQ); \$QP=switch(\$rQ,\$AQ*\$NQ*\$X^(\$NQM),(\$AQ*\$NQ*\$X^(\$NQM)+\$BQ),(2*\$AQ*\$X+\$BQ)); \$rT=rint(2); \$T=switch(\$rT,\$CT*"e"^(\$K*\$X)+\$BT,\$CT*"e"^(\$K*\$X)+\$BT*\$X); \$TP=switch(\$rT,\$CT*\$K*"e"^(\$K*\$X),(\$CT*\$K*"e"^(\$K*\$X)+\$BT)); \$rS=rint(3); \$S=switch(\$rS,sin(\$AS*\$X),cos(\$AS*\$X),tan(\$AS*\$X)); \$SP=switch(\$rS,\$AS*cos(\$AS*\$X),-\$AS*sin(\$AS*\$X),\$AS*(sec(\$AS*\$X))^2); \$SPf=switch(\$rS,cos(\$AS*\$X),sin(\$AS*\$X),(sec(\$AS*\$X))^2); \$SPc=switch(\$rS,\$AS,-\$AS,\$AS); \$rF=rint(3); \$F=switch(\$rF,\$P,\$Q,"\$T"); \$FP=switch(\$rF,\$PP,\$QP,"\$TP"); \$r=rint(2); \$function=switch(\$r,"\$F"/\$S,\$S/"\$F"); \$num=switch(\$r,("\$FP")*\$S-\$SPc*("\$F")*\$SPf,\$SPc*("\$F")*\$SPf-("\$FP")*\$S); \$den=switch(\$r,(\$S)^2,("\$F")^2); \$answer="(\$num)/\$den";@ qu.3.2.question=Find the derivative of \${mathml("\$function")}.@ qu.3.2.answer=\$answer@ qu.4.topic=4-compositions@ qu.4.1.mode=Formula@ qu.4.1.comment=The answer is \${mathml("\$answer")}.@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$rP=rint(2); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X); \$PP=switch(\$rP,\$N*\$X^(\$NM),(\$N*\$X^(\$NM)+\$B)); \$rS=rint(2); \$S=switch(\$rS,sin(\$A*\$X),cos(\$A*\$X)); \$SP=switch(\$rS,\$A*cos(\$A*\$X),-\$A*sin(\$A*\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$r=rint(3); \$function=switch(\$r,sqrt(\$P),sqrt(\$S),sqrt("\$T")); \$answer=switch(\$r,(\$PP)/(2*sqrt(\$P)),(\$SP)/(2*sqrt(\$S)),("\$TP")/(2*sqrt("\$T")));@ qu.4.1.question=Find the derivative of \${mathml("\$function")}.@ qu.4.1.answer=\$answer@ qu.4.2.mode=Formula@ qu.4.2.comment=The answer is \${mathml("\$answer")}.@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$rS=rint(2); \$S=switch(\$rS,sin(\$A*\$X),cos(\$A*\$X)); \$SP=switch(\$rS,\$A*cos(\$A*\$X),-\$A*sin(\$A*\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$r=rint(2); \$function=switch(\$r,(\$S)^\$N,("\$T")^\$N); \$answer=switch(\$r,\$N*\$SP*(\$S)^\$NM,\$N*"\$TP"*("\$T")^\$NM);@ qu.4.2.question=Find the derivative of \${mathml("\$function")}.@ qu.4.2.answer=\$answer@ qu.4.3.mode=Formula@ qu.4.3.comment=The answer is \${mathml("\$answer")}.@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$rQ=rint(3); \$Q=switch(\$rQ,\$A*\$X^\$N+\$B,\$A*\$X^\$N+\$B*\$X,sqrt(\$X)+\$B); \$QP=switch(\$rQ,\$A*\$N*\$X^(\$NM),(\$A*\$N*\$X^(\$NM)+\$B),1/(2*sqrt(\$X))); \$rS=rint(2); \$S=switch(\$rS,sin(\$A*\$X),cos(\$A*\$X)); \$SP=switch(\$rS,\$A*cos(\$A*\$X),-\$A*sin(\$A*\$X)); \$r=rint(2); \$function=switch(\$r,"e"^(\$Q),"e"^(\$S)); \$answer=switch(\$r,(\$QP)*"\$function",(\$SP)*"\$function");@ qu.4.3.question=Find the derivative of \${mathml("\$function")}.@ qu.4.3.answer=\$answer@ qu.4.4.mode=Formula@ qu.4.4.comment=The answer is \${mathml("\$answer")}.@ qu.4.4.editing=useHTML@ qu.4.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$rQ=rint(3); \$Q=switch(\$rQ,\$A*\$X^\$N+\$B,\$A*\$X^\$N+\$B*\$X,sqrt(\$X)+\$B); \$QP=switch(\$rQ,\$A*\$N*\$X^(\$NM),(\$A*\$N*\$X^(\$NM)+\$B),1/(2*sqrt(\$X))); \$rS=rint(2); \$S=switch(\$rS,sin(\$A*\$X),cos(\$A*\$X)); \$SP=switch(\$rS,\$A*cos(\$A*\$X),-\$A*sin(\$A*\$X)); \$r=rint(2); \$function=switch(\$r,ln(\$Q),ln(\$S)); \$answer=switch(\$r,(\$QP)/(\$Q),(\$SP)/(\$S));@ qu.4.4.question=Find the derivative of \${mathml("\$function")}.@ qu.4.4.answer=\$answer@ qu.4.5.mode=Formula@ qu.4.5.comment=The answer is \${mathml("\$answer")}.@ qu.4.5.editing=useHTML@ qu.4.5.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$rQ=rint(3); \$Q=switch(\$rQ,\$A*\$X^\$N+\$B,\$A*\$X^\$N+\$B*\$X,sqrt(\$X)+\$B); \$QP=switch(\$rQ,\$A*\$N*\$X^(\$NM),(\$A*\$N*\$X^(\$NM)+\$B),1/(2*sqrt(\$X))); \$rU=rint(3); \$U=switch(\$rU,\$A*"e"^(\$K*\$X)+\$B,\$A*ln(\$X),\$N^\$X); \$UP=switch(\$rU,\$A*\$K*"e"^(\$K*\$X),\$A/\$X,"ln(\$N)"*\$N^\$X); \$r=rint(4); \$function=switch(\$r,sin(\$Q),cos(\$Q),sin("\$U"),cos("\$U")); \$answer=switch(\$r,(\$QP)*cos(\$Q),-(\$QP)*sin(\$Q),("\$UP")*cos("\$U"),("-\$UP")*sin("\$U"));@ qu.4.5.question=Find the derivative of \${mathml("\$function")}.@ qu.4.5.answer=\$answer@ qu.5.topic=5-quotients with an embedded product@ qu.5.1.mode=Formula@ qu.5.1.comment=The answer is \${mathml("\$answer")}.@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$n=range(2,6); \$nm=\$n-1; \$Q=\$X^\$N; \$QP=\$N*\$X^(\$NM); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rU=rint(2); \$U=switch(\$rU,"e"^\$X,ln(\$X)); \$UP=switch(\$rU,"\$U",\$X^(-1)); \$rP=rint(2); \$P=switch(\$rP,\$X^\$n+\$B,\$X^\$n+\$B*\$X); \$PP=switch(\$rP,\$n*\$X^(\$nm),\$n*\$X^(\$nm)+\$B); \$rF=rint(3); \$F=switch(\$rF,\$Q*"\$U",\$Q*\$S,"\$U"*\$S); \$fp=switch(\$rF,\$QP*"\$U"+\$Q*"\$UP",\$QP*\$S+\$Q*(\$SP),"\$UP"*\$S+"\$U"*(\$SP)); \$FP=if(eq(\$rU-\$rF,1),\$QP*\$U+\$X^(\$NM),"\$fp"); \$function=("\$F")/(\$P); \$r=if(eq(\$rP,1),3,\$rF); \$num=("\$FP")*(\$P)-switch(\$r,\$n*\$X^(\$nm+\$N)*"\$U",\$n*\$X^(\$nm+\$N)*\$S,\$PP*("\$F"),("\$F")*(\$PP)); \$answer="(\$num)/(\$P)^2";@ qu.5.1.question=Find the derivative of \${mathml("\$function")}.@ qu.5.1.answer=\$answer@ qu.5.2.mode=Formula@ qu.5.2.comment=The answer is \${mathml("\$answer")}.@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$n=range(2,6); \$nm=\$n-1; \$Q=\$X^\$N; \$QP=\$N*\$X^(\$NM); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rU=rint(2); \$U=switch(\$rU,ln(\$X),"e"^\$X); \$UP=switch(\$rU,\$X^(-1),"\$U"); \$rR=rint(2); \$R=switch(\$rR,sin(\$a*\$X),cos(\$a*\$X)); \$RPf=switch(\$rR,cos(\$a*\$X),-sin(\$a*\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$r=rint(3); \$F=switch(\$r,\$Q*"\$U",\$Q*\$S,\$Q); \$fp=switch(\$r,\$QP*"\$U"+\$Q*"\$UP",\$QP*\$S+\$Q*(\$SP),\$QP); \$FP=if(eq(\$rU+\$r,0),\$QP*\$U+\$X^(\$NM),"\$fp"); \$G=switch(\$r,\$R,"\$T","\$U"*\$S); \$GP=switch(\$r,\$a*\$RPf,"\$TP","\$UP"*\$S+"\$U"*(\$SP)); \$function=("\$F")/("\$G"); \$num=if(eq(\$r+\$rR,0),("\$FP")*(\$G)-\$a*("\$F")*(\$RPf),"(\$FP)*(\$G)-(\$F)*(\$GP)"); \$answer="(\$num)/(\$G)^2";@ qu.5.2.question=Find the derivative of \${mathml("\$function")}.@ qu.5.2.answer=\$answer@ qu.6.topic=6-products with a composite factor@ qu.6.1.mode=Formula@ qu.6.1.comment=The answer is \${mathml("\$answer")}.@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=\$X="x"; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$V=range(2,6); \$M=range(2,6); \$D=range(-2,2); \$rF=rint(5); \$F=switch(\$rF,\$X^\$M,\$X^\$M+\$D,"e"^(-\$V*\$X),sin(\$X),cos(\$X)); \$FP=switch(\$rF,\$M*\$X^(\$M-1),\$M*\$X^(\$M-1),-\$V*"\$F",cos(\$X),-sin(\$X)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X); \$PP=switch(\$rP,\$N*\$X^(\$NM),(\$N*\$X^(\$NM)+\$B)); \$rG=rint(2); \$G=switch(\$rG,(\$P)^(-\$C),sqrt(\$P)); \$GP=switch(\$rG,-\$C*(\$P)^(-\$C-1)*(\$PP),(\$PP)/(2*sqrt(\$P))); \$function=("\$F")*(\$G); \$answer=("\$FP")*(\$G)+("\$F")*(\$GP);@ qu.6.1.question=Find the derivative of \${mathml("\$function")}.@ qu.6.1.answer=\$answer@ qu.6.2.mode=Formula@ qu.6.2.comment=The answer is \${mathml("\$answer")}.@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=\$X="x"; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$V=range(2,6); \$M=range(2,6); \$D=range(-2,2); \$rF=rint(5); \$F=switch(\$rF,\$X^\$M,\$X^\$M+\$D,"e"^(-\$V*\$X),sin(\$X),cos(\$X)); \$FP=switch(\$rF,\$M*\$X^(\$M-1),\$M*\$X^(\$M-1),-\$V*"\$F",cos(\$X),-sin(\$X)); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$r=rint(2); \$G=switch(\$r,(\$S)^\$N,("\$T")^\$N); \$GP=switch(\$r,\$N*\$SP*(\$S)^\$NM,\$N*"\$TP"*("\$T")^\$NM); \$function=("\$F")*("\$G"); \$answer=("\$FP")*("\$G")+("\$F")*("\$GP");@ qu.6.2.question=Find the derivative of \${mathml("\$function")}.@ qu.6.2.answer=\$answer@ qu.6.3.mode=Formula@ qu.6.3.comment=The answer is \${mathml("\$answer")}.@ qu.6.3.editing=useHTML@ qu.6.3.algorithm=\$X="x"; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$V=range(2,6); \$M=range(2,6); \$D=range(-2,2); \$rF=rint(4); \$F=switch(\$rF,\$X^\$M,\$X^\$M+\$D,sin(\$X),cos(\$X)); \$FP=switch(\$rF,\$M*\$X^(\$M-1),\$M*\$X^(\$M-1),cos(\$X),-sin(\$X)); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$r=rint(2); \$G=switch(\$r,"e"^(\$X^\$N),"e"^(\$S)); \$GP=switch(\$r,\$N*\$X^(\$NM)*"\$G",(\$SP)*"\$G"); \$function=if(gt((1-\$r)*\$rF,1),"\$G*(\$F)","(\$F)*\$G"); \$ans=if(gt((1-\$r)*\$rF,1),"\$GP"*\$F+("\$G")*(\$FP),"\$FP*\$G"+(\$F)*("\$GP")); \$answer=switch(\$rF+2*\$r,(\$FP+\$N*\$X^(\$NM+\$M))*"\$G",\$FP*"\$G"+\$N*\$X^(\$NM)*(\$F)*"\$G","\$ans","\$ans","\$ans","\$ans");@ qu.6.3.question=Find the derivative of \${mathml("\$function")}.@ qu.6.3.answer=\$answer@ qu.6.4.mode=Formula@ qu.6.4.comment=The answer is \${mathml("\$answer")}.@ qu.6.4.editing=useHTML@ qu.6.4.algorithm=\$X="x"; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$V=range(2,6); \$M=range(2,6); \$D=range(-2,2); \$rF=rint(5); \$F=switch(\$rF,\$X^\$M,\$X^\$M+\$D,"e"^(-\$V*\$X),sin(\$X),cos(\$X)); \$FP=switch(\$rF,\$M*\$X^(\$M-1),\$M*\$X^(\$M-1),-\$V*"\$F",cos(\$X),-sin(\$X)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X,\$C*\$X^2+\$B*\$X+\$A); \$PP=switch(\$rP,\$N*\$X^(\$NM),(\$N*\$X^(\$NM)+\$B),2*\$C*\$X+\$B); \$G=ln(\$P); \$GP=(\$PP)/(\$P); \$function=("\$F")*(\$G); \$answer=("\$FP")*(\$G)+("\$F")*(\$GP);@ qu.6.4.question=Find the derivative of \${mathml("\$function")}.@ qu.6.4.answer=\$answer@ qu.6.5.mode=Formula@ qu.6.5.comment=The answer is \${mathml("\$answer")}.@ qu.6.5.editing=useHTML@ qu.6.5.algorithm=\$X="x"; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$V=range(2,6); \$M=range(2,6); \$MM=\$M-1; \$D=range(-2,2); \$rF=rint(3); \$F=switch(\$rF,\$X^\$M,\$X^\$M+\$D,"e"^(-\$V*\$X)); \$FP=switch(\$rF,\$M*\$X^(\$MM),\$M*\$X^(\$MM),-\$V*"\$F"); \$P=\$X^\$N; \$PP=\$N*\$X^(\$NM); \$rU=rint(2); \$U=switch(\$rU,"e"^(-\$C*\$X),\$A*ln(\$X)); \$UP=switch(\$rU,-\$C*"\$U",\$A/\$X); \$rG=rint(4); \$G=switch(\$rG,sin(\$P),cos(\$P),sin("\$U"),cos("\$U")); \$GP=switch(\$rG,cos(\$P)*(\$PP),-sin(\$P)*(\$PP),cos("\$U")*("\$UP"),-sin("\$U")*("\$UP")); \$function=("\$F")*("\$G"); \$ans=("\$FP")*("\$G")+("\$F")*("\$GP"); \$r=if(gt(\$rG,1),4,if(eq(\$rF,0),\$rG,2+\$rG)); \$answer=switch(\$r,\$FP*\$G+\$N*\$X^(\$MM+\$N)*cos(\$P),\$FP*\$G-\$N*\$X^(\$MM+\$N)*sin(\$P),("\$FP")*\$G+\$PP*("\$F")*cos(\$P),("\$FP")*\$G-\$PP*("\$F")*sin(\$P),"\$ans");@ qu.6.5.question=Find the derivative of \${mathml("\$function")}.@ qu.6.5.answer=\$answer@ qu.7.topic=7-compositions of products@ qu.7.1.mode=Formula@ qu.7.1.comment=The answer is \${mathml("\$answer")}.@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$N=range(2,6); \$M=range(2,6); \$J=range(3,9); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1)*(\$M-\$N),0)); \$NM=\$N-1; \$MM=\$M-1; \$JM=\$J-1; \$r=rint(2); \$rP=rint(4); \$rH=rint(6); condition:not(eq(\$rP,\$rH)); \$F=switch(\$rP,\$X^\$N*sin(\$X),\$X^\$N*cos(\$X),\$X^\$N*ln(\$X),\$X^\$N*"e"^(-\$A*\$X)); \$FP=switch(\$rP,\$N*\$X^\$NM*sin(\$X)+\$X^\$N*cos(\$X),\$N*\$X^\$NM*cos(\$X)-\$X^\$N*sin(\$X),\$N*\$X^\$NM*ln(\$X)+\$X^\$NM,(\$N*\$X^\$NM-\$A*\$X^\$N)*"e"^(-\$A*\$X)); \$G=switch(\$rP,"e"^(\$X)*sin(\$X),"e"^(\$X)*cos(\$X),"e"^(\$X)*ln(\$X),\$X^\$N*"e"^(-\$A*\$X)); \$GP=switch(\$rP,"e"^(\$X)*sin(\$X)+"e"^(\$X)*cos(\$X),"e"^(\$X)*cos(\$X)-"e"^(\$X)*sin(\$X),"e"^(\$X)*(ln(\$X)+\$X^(-1)),(\$N*\$X^\$NM-\$A*\$X^\$N)*"e"^(-\$A*\$X)); \$P=switch(\$r,"\$F","\$G"); \$PP=switch(\$r,"\$FP","\$GP"); \$H=switch(\$rH,\$B*sin(\$X),\$B*cos(\$X),\$B*ln(\$X),"e"^(\$K*\$X),\$B*\$X^\$M,\$B*"pi"^\$M); \$HP=switch(\$rH,\$B*cos(\$X),-\$B*sin(\$X),\$B/\$X,\$K*"\$H",\$B*\$M*\$X^\$MM,0); \$function=("\$P+\$H")^\$J; \$answer="\$J*(\$P+\$H)^\$JM*(\$PP+\$HP)";@ qu.7.1.question=Find the derivative of \${mathml("\$function")}.@ qu.7.1.answer=\$answer@ qu.7.2.mode=Formula@ qu.7.2.comment=The answer is \${mathml("\$answer")}.@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$N=range(2,6); \$M=range(2,6); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1)*(\$M-\$N),0)); \$NM=\$N-1; \$MM=\$M-1; \$r=rint(2); \$rP=rint(3); \$rH=rint(5); condition:not(eq(\$rP,\$rH)); \$F=switch(\$rP,\$X^\$N*sin(\$X),\$X^\$N*cos(\$X),\$X^\$N*"e"^(-\$A*\$X)); \$FP=switch(\$rP,\$N*\$X^\$NM*sin(\$X)+\$X^\$N*cos(\$X),\$N*\$X^\$NM*cos(\$X)-\$X^\$N*sin(\$X),(\$N*\$X^\$NM-\$A*\$X^\$N)*"e"^(-\$A*\$X)); \$G=switch(\$rP,"e"^(\$X)*sin(\$X),"e"^(\$X)*cos(\$X),\$X^\$N*"e"^(-\$A*\$X)); \$GP=switch(\$rP,"e"^(\$X)*sin(\$X)+"e"^(\$X)*cos(\$X),"e"^(\$X)*cos(\$X)-"e"^(\$X)*sin(\$X),(\$N*\$X^\$NM-\$A*\$X^\$N)*"e"^(-\$A*\$X)); \$P=switch(\$r,"\$F","\$G"); \$PP=switch(\$r,"\$FP","\$GP"); \$H=switch(\$rH,\$B*sin(\$X),\$B*cos(\$X),"e"^(\$K*\$X),\$B*\$X^\$M,\$B*"pi"^\$M); \$HP=switch(\$rH,\$B*cos(\$X),-\$B*sin(\$X),\$K*"\$H",\$B*\$M*\$X^\$MM,0); \$function=ln("\$P+\$H"); \$answer="(\$PP+\$HP)/(\$P+\$H)";@ qu.7.2.question=Find the derivative of \${mathml("\$function")}.@ qu.7.2.answer=\$answer@ qu.7.3.mode=Formula@ qu.7.3.comment=The answer is \${mathml("\$answer")}.@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$N=range(2,6); \$NM=\$N-1; \$rF=rint(2); \$F=switch(\$rF,\$X^\$N*ln(\$X),\$X^\$N*"e"^(\$A*\$X)); \$FP=switch(\$rF,\$N*\$X^\$NM*ln(\$X)+\$X^\$NM,(\$N*\$X^\$NM+\$A*\$X^\$N)*"e"^(\$A*\$X)); \$r=rint(2); \$function=switch(\$r,sin("\$F"),cos("\$F")); \$answer=switch(\$r,("\$FP")*cos("\$F"),-("\$FP")*sin("\$F"));@ qu.7.3.question=Find the derivative of \${mathml("\$function")}.@ qu.7.3.answer=\$answer@ qu.8.topic=8-compositions of compositions@ qu.8.1.mode=Formula@ qu.8.1.comment=The answer is \${mathml("\$answer")}.@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(1,9); \$B=range(-9,9); \$K=range(-6,6); \$N=range(2,6); \$NM=\$N-1; \$M=range(3,8); \$MM=\$M-1; condition:not(eq(\$K*(\$K-1)*\$B*(\$N-\$M),0)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X,\$X^2+\$B*\$X+\$A); \$PP=switch(\$rP,\$N*\$X^(\$NM),\$N*\$X^(\$NM)+\$B,2*\$X+\$B); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$A*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$A*"e"^(-\$A*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rF=rint(6); \$F=switch(\$rF,ln(\$P),ln(\$S),sin(\$P),cos(\$P),sin("\$T"),cos("\$T")); \$FP=switch(\$rF,(\$PP)/(\$P),(\$SP)/(\$S),cos(\$P)*(\$PP),-sin(\$P)*(\$PP),cos("\$T")*("\$TP"),-sin("\$T")*("\$TP")); \$function=("\$F")^\$M; \$answer=\$M*("\$F")^\$MM*("\$FP");@ qu.8.1.question=Find the derivative of \${mathml("\$function")}.@ qu.8.1.answer=\$answer@ qu.8.2.mode=Formula@ qu.8.2.comment=The answer is \${mathml("\$answer")}.@ qu.8.2.editing=useHTML@ qu.8.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(1,9); \$B=range(-9,9); \$K=range(-6,6); \$N=range(2,6); \$NM=\$N-1; condition:not(eq(\$K*(\$K-1)*\$B,0)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X,\$X^2+\$B*\$X+\$A); \$PP=switch(\$rP,\$N*\$X^(\$NM),\$N*\$X^(\$NM)+\$B,2*\$X+\$B); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rF=rint(3); \$F=switch(\$rF,(\$S)^\$N,sin(\$P),cos(\$P)); \$FP=switch(\$rF,\$N*(\$S)^\$NM*(\$SP),cos(\$P)*(\$PP),-sin(\$P)*(\$PP)); \$function="e"^(\$F); \$answer="e"^(\$F)*(\$FP);@ qu.8.2.question=Find the derivative of \${mathml("\$function")}.@ qu.8.2.answer=\$answer@ qu.8.3.mode=Formula@ qu.8.3.comment=The answer is \${mathml("\$answer")}.@ qu.8.3.editing=useHTML@ qu.8.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(1,9); \$B=range(-9,9); \$K=range(-6,6); \$N=range(2,6); \$NM=\$N-1; condition:not(eq(\$K*(\$K-1)*\$B,0)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X,\$X^2+\$B*\$X+\$A); \$PP=switch(\$rP,\$N*\$X^(\$NM),\$N*\$X^(\$NM)+\$B,2*\$X+\$B); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$A*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$A*"e"^(-\$A*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rF=rint(4); \$F=switch(\$rF,sin(\$P),cos(\$P),sin("\$T"),cos("\$T")); \$FP=switch(\$rF,cos(\$P)*(\$PP),-sin(\$P)*(\$PP),cos("\$T")*("\$TP"),-sin("\$T")*("\$TP")); \$function=ln("\$F"); \$answer=("\$FP")/("\$F");@ qu.8.3.question=Find the derivative of \${mathml("\$function")}.@ qu.8.3.answer=\$answer@ qu.8.4.mode=Formula@ qu.8.4.comment=The answer is \${mathml("\$answer")}.@ qu.8.4.editing=useHTML@ qu.8.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(1,9); \$B=range(-9,9); \$K=range(-6,6); \$N=range(2,6); \$NM=\$N-1; condition:not(eq(\$K*(\$K-1)*\$B,0)); \$rP=rint(3); \$P=switch(\$rP,\$X^\$N+\$B,\$X^\$N+\$B*\$X,\$X^2+\$B*\$X+\$A); \$PP=switch(\$rP,\$N*\$X^(\$NM),\$N*\$X^(\$NM)+\$B,2*\$X+\$B); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$A*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$A*"e"^(-\$A*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rF=rint(3); \$F=switch(\$rF,"\$T"^\$N,"e"^(\$P),ln(\$P)); \$FP=switch(\$rF,\$N*("\$TP")*"\$T"^(\$NM),(\$PP)*"e"^(\$P),(\$PP)/(\$P)); \$r=rint(2); \$function=switch(\$r,"sin","cos"); \$answer=switch(\$r,("\$FP")*cos("\$F"),"(\$FP)"*(-sin("\$F")));@ qu.8.4.question=Find the derivative of $\mathrm{function}\text{\hspace{0.17em}}\left(\left\{mathml\left("F","notags"\right)\right\}\right)$.@ qu.8.4.answer=\$answer@ qu.9.topic=9-quotients with an embedded composition@ qu.9.1.mode=Formula@ qu.9.1.comment=The answer is \${mathml("\$answer")}.@ qu.9.1.editing=useHTML@ qu.9.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,6); \$nm=\$n-1; \$Q=\$A*\$X^\$N; \$QP=\$A*\$N*\$X^(\$NM); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rP=rint(2); \$P=switch(\$rP,\$a*\$X^\$n+\$b,\$a*\$X^\$n+\$b*\$X); \$PP=switch(\$rP,\$a*\$n*\$X^(\$nm),\$a*\$n*\$X^(\$nm)+\$b); \$rF=rint(5); \$F=switch(\$rF,\$S^\$N,ln(\$Q+\$B),ln(\$S),sin(\$Q),cos(\$Q)); \$FP=switch(\$rF,\$N*\$SP*(\$S)^\$NM,(\$QP)/(\$Q+\$B),\$SP/\$S,(\$QP)*cos(\$Q),-(\$QP)*sin(\$Q)); \$function=(\$F)/(\$P); \$answer=switch(\$rP,((\$FP)*(\$P)-\$PP*(\$F))/(\$P)^2,((\$FP)*(\$P)-(\$F)*(\$PP))/(\$P)^2);@ qu.9.1.question=Find the derivative of \${mathml("\$function")}.@ qu.9.1.answer=\$answer@ qu.9.2.mode=Formula@ qu.9.2.comment=The answer is \${mathml("\$answer")}.@ qu.9.2.editing=useHTML@ qu.9.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,6); \$nm=\$n-1; \$Q=\$A*\$X^\$N; \$QP=\$A*\$N*\$X^(\$NM); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rU=rint(2); \$U=switch(\$rU,"e"^(-\$C*\$X),ln(\$X)); \$UP=switch(\$rU,-\$C*"\$U",1/\$X); \$rP=rint(2); \$P=switch(\$rP,\$a*\$X^\$n+\$b,\$a*\$X^\$n+\$b*\$X); \$PP=switch(\$rP,\$a*\$n*\$X^(\$nm),\$a*\$n*\$X^(\$nm)+\$b); \$rF=rint(5); \$F=switch(\$rF,("\$T")^\$N,"e"^(\$Q),"e"^\$S,sin("\$U"),cos("\$U")); \$FP=switch(\$rF,\$N*("\$TP")*("\$T")^\$NM,(\$QP)*"e"^(\$Q),\$SP*"e"^\$S,"\$UP"*cos("\$U"),-"\$UP"*sin("\$U")); \$function=("\$F")/(\$P); \$answer=switch(\$rP,(("\$FP")*(\$P)-\$PP*("\$F"))/(\$P)^2,(("\$FP")*(\$P)-("\$F")*(\$PP))/(\$P)^2);@ qu.9.2.question=Find the derivative of \${mathml("\$function")}.@ qu.9.2.answer=\$answer@ qu.9.3.mode=Formula@ qu.9.3.comment=The answer is \${mathml("\$answer")}.@ qu.9.3.editing=useHTML@ qu.9.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,6); \$nm=\$n-1; \$Q=\$A*\$X^\$N; \$QP=\$A*\$N*\$X^(\$NM); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rG=rint(5); \$G=switch(\$rG,\$S^\$N,ln(\$Q+\$B),ln(\$S),sin(\$Q),cos(\$Q)); \$GP=switch(\$rG,\$N*\$SP*(\$S)^\$NM,(\$QP)/(\$Q+\$B),\$SP/\$S,(\$QP)*cos(\$Q),-(\$QP)*sin(\$Q)); \$function=(\$G)/("\$T"); \$answer=((\$GP)*("\$T")-(\$G)*("\$TP"))/("\$T")^2;@ qu.9.3.question=Find the derivative of \${mathml("\$function")}.@ qu.9.3.answer=\$answer@ qu.9.4.mode=Formula@ qu.9.4.comment=The answer is \${mathml("\$answer")}.@ qu.9.4.editing=useHTML@ qu.9.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,6); \$nm=\$n-1; \$Q=\$A*\$X^\$N; \$QP=\$A*\$N*\$X^(\$NM); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rR=rint(2); \$R=switch(\$rR,sin(\$a*\$X),cos(\$a*\$X)); \$RPf=switch(\$rR,cos(\$a*\$X),-sin(\$a*\$X)); \$rF=rint(3); \$F=switch(\$rF,("\$T")^\$N,"e"^(\$Q),ln(\$Q+\$B)); \$FP=switch(\$rF,\$N*("\$TP")*("\$T")^\$NM,(\$QP)*"e"^(\$Q),(\$QP)/(\$Q+\$B)); \$function=("\$F")/(\$R); \$answer=(("\$FP")*(\$R)-\$a*("\$F")*(\$RPf))/(\$R)^2;@ qu.9.4.question=Find the derivative of \${mathml("\$function")}.@ qu.9.4.answer=\$answer@ qu.9.5.mode=Formula@ qu.9.5.comment=The answer is \${mathml("\$answer")}.@ qu.9.5.editing=useHTML@ qu.9.5.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$A=range(2,9); \$B=range(-9,9); \$C=range(2,6); \$K=range(-6,6); condition:not(eq(\$K*(\$K-1)*\$B,0)); \$N=range(2,6); \$NM=\$N-1; \$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,6); \$nm=\$n-1; \$rP=rint(2); \$P=switch(\$rP,\$a*\$X^\$n+\$b,\$a*\$X^\$n+\$b*\$X); \$PP=switch(\$rP,\$a*\$n*\$X^(\$nm),\$a*\$n*\$X^(\$nm)+\$b); \$rR=rint(2); \$R=switch(\$rR,sin(\$a*\$X),cos(\$a*\$X)); \$RP=switch(\$rR,\$a*cos(\$a*\$X),-\$a*sin(\$a*\$X)); \$rS=rint(2); \$S=switch(\$rS,sin(\$X),cos(\$X)); \$SP=switch(\$rS,cos(\$X),-sin(\$X)); \$rT=rint(2); \$T=switch(\$rT,"e"^(-\$C*\$X)+\$B,"e"^(\$K*\$X)+\$B*\$X); \$TP=switch(\$rT,-\$C*"e"^(-\$C*\$X),(\$K*"e"^(\$K*\$X)+\$B)); \$rF=rint(2); \$F=switch(\$rF,\$P,"\$T"); \$FP=switch(\$rF,\$PP,"\$TP"); \$rG=rint(3); \$G=switch(\$rG,ln(\$S),sin(\$A*\$X^\$N),cos(\$A*\$X^\$N)); \$function=("\$F")/(\$G); \$answer=switch(\$rG,(("\$FP")*(\$G)-("\$F")*(\$SP/\$S))/(\$G)^2,(("\$FP")*(\$G)-\$A*\$N*\$X^(\$NM)*("\$F")*cos(\$A*\$X^\$N))/(\$G)^2,(("\$FP")*(\$G)+\$A*\$N*\$X^(\$NM)*("\$F")*sin(\$A*\$X^\$N))/(\$G)^2);@ qu.9.5.question=Find the derivative of \${mathml("\$function")}.@ qu.9.5.answer=\$answer@ qu.10.topic=10-implicit differentiation@ qu.10.1.mode=Formula@ qu.10.1.comment=The answer is \${mathml("\$answer")}.@ qu.10.1.editing=useHTML@ qu.10.1.algorithm=\$A=range(2,9); \$B=range(-3,3); \$C=range(1,9); \$J=range(3,6); \$M=range(3,6); \$N=range(3,6); \$P=range(3,6); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1),0)); \$rG=rint(3); \$G=switch(\$rG,"e"^(y),sin(y),cos(y)); \$GP=switch(\$rG,"\$G",cos(y),-sin(y)); \$rR=rint(4); \$R=switch(\$rR,x^\$N,"e"^(\$K*x),sin(\$A*x),cos(\$A*x)); \$RP=switch(\$rR,\$N*x^(\$N-1),\$K*"\$R",\$A*cos(\$A*x),-\$A*sin(\$A*x)); \$function="\$R+\$G+x^\$J*y^\$M"; \$answer="(-\$RP-\$J*x^(\$J-1)*y^\$M)/(\$GP+\$M*x^\$J*y^(\$M-1))";@ qu.10.1.question=Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ for \${mathml("\$function")} $=C$.@ qu.10.1.answer=\$answer@ qu.10.2.mode=Formula@ qu.10.2.comment=The answer is \${mathml("\$answer")}.@ qu.10.2.editing=useHTML@ qu.10.2.algorithm=\$A=range(2,9); \$B=range(-3,3); \$C=range(1,9); \$J=range(3,6); \$M=range(3,6); \$N=range(3,6); \$P=range(3,6); \$K=range(-6,6); condition:not(eq(\$B*\$K*(\$K-1),0)); \$rG=rint(3); \$G=switch(\$rG,"e"^(y),sin(y),cos(y)); \$GP=switch(\$rG,"\$G",cos(y),-sin(y)); \$rR=rint(4); \$R=switch(\$rR,x^\$N,"e"^(\$K*x),sin(\$A*x),cos(\$A*x)); \$RP=switch(\$rR,\$N*x^(\$N-1),\$K*"\$R",\$A*cos(\$A*x),-\$A*sin(\$A*x)); \$function="\$B*y^\$M+\$R+x^\$J*\$G"; \$answer="(-\$RP-\$J*x^(\$J-1)*\$G)/(\$B*\$M*y^(\$M-1)+x^\$J*\$GP)";@ qu.10.2.question=Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ for \${mathml("\$function")} $=C$.@ qu.10.2.answer=\$answer@ qu.10.3.mode=Formula@ qu.10.3.comment=The answer is \${mathml("\$answer")}.@ qu.10.3.editing=useHTML@ qu.10.3.algorithm=\$A=range(2,9); \$B=range(-3,3); \$C=range(1,9); \$J=range(3,6); \$M=range(3,6); \$N=range(3,6); \$P=range(3,6); condition:not(eq(\$B*(\$N-4),0)); \$rR=rint(2); \$R=switch(\$rR,x^\$N,"e"^x); \$RP=switch(\$rR,\$N*x^(\$N-1),"\$R"); \$r=rint(2); \$function=switch(\$r,sin(y^\$M+x^\$P),cos(y^\$M+x^\$P)); \$FP=switch(\$r,cos(y^\$M+x^\$P),sin(y^\$M+x^\$P)); \$answer=switch(\$r,("\$RP"-\$P*x^(\$P-1)*\$FP)/(\$M*y^(\$M-1)*\$FP),("\$RP"+\$P*x^(\$P-1)*\$FP)/(-\$M*y^(\$M-1)*\$FP));@ qu.10.3.question=Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ for \${mathml("\$function")} $=$ \${mathml("\$R")}.@ qu.10.3.answer=\$answer@