qu.1.topic=1-power functions and sums@ qu.1.1.mode=Formula@ qu.1.1.comment=Use the power rule and the sum rule.@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=\$p=range(-3,3); \$q=range(1,3,2); \$a=range(-3,3); \$b=range(-2,2); \$c=range(1,6); \$d=range(1,6); condition:not(eq(\$p*(\$p-1)*\$a*\$b,0)); \$answer=\$a*\$p*x^(\$p-1)-\$b*\$q*x^(-\$q/2-1)+\$c;@ qu.1.1.question=Find the derivative of \${mathml(\$a*x^\$p+2*\$b*x^(-\$q/2)+\$c*x+\$d)}@ qu.1.1.answer=\$answer@ qu.2.topic=2-second derivatives@ qu.2.1.mode=Formula@ qu.2.1.comment=The answer is \${mathml(\$answer)}.@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=\$p=range(1,7,2); \$q=range(-4,-1); \$a=range(1,3); \$b=range(1,10); \$answer=\$p*(\$p-2)/4*x^(\$p/2-2)-\$a*\$q*(\$q-1)*x^(\$q-2);@ qu.2.1.question=Find the second derivative of \${mathml(f)}(\${mathml(x)})=\${mathml(x^(\$p/2)-\$a*x^\$q+\$b*x)}.@ 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=\$p=range(3,5); \$q=range(1,4); \$a=range(1,10); \$b=range(1,10); \$answer=(\$p+\$q)*(\$p+\$q-1)*x^(\$p+\$q-2)+\$a*\$p*(\$p-1)*x^(\$p-2);@ qu.2.2.question=Find the second derivative of \${mathml(y)}=\${mathml(x^(\$p)*(x^\$q+\$a)+\$b*"pi"^2)}.@ qu.2.2.answer=\$answer@ qu.3.topic=3-product rule@ qu.3.1.mode=Formula@ qu.3.1.comment=Look up the product rule! Use \$f for "f", \$g for "g", \$k for "f'" and \$h for "g'".@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=\$f=switch(rint(2),"u","v"); \$g=switch(rint(2),"y","z"); \$h=switch(rint(3),"q","r","s"); \$k=switch(rint(2),"w","p"); \$answer=\$k*\$g+\$f*\$h;@ qu.3.1.question=Suppose \${mathml(\$f)} and \${mathml(\$g)} are functions of \${mathml(x)}, with ${\mathrm{f}}^{\prime }=\mathrm{k}$ and ${\mathrm{g}}^{\prime }=\mathrm{h}$. What is the derivative of \${mathml(\$f*\$g)}?@ qu.3.1.answer=\$answer@ qu.3.2.mode=Formula@ qu.3.2.comment=Use the product rule. The answer is \${mathml(\$answer)}.@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=\$a=range(2,18,2); \$b=range(-19,19,2); \$c=range(1,9,2); \$d=range(1,19); \$e=range(2,18,2); \$answer=\$a*(\$c*x^2+\$d*x-\$e)+(\$a*x+\$b)*(2*\$c*x+\$d);@ qu.3.2.question=Find the derivative of \${mathml((\$a*x+\$b)*(\$c*x^2+\$d*x-\$e))}.@ qu.3.2.answer=\$answer@ qu.3.3.mode=Formula@ qu.3.3.comment=Use the product rule. The answer is \${mathml(\$answer)}.@ qu.3.3.editing=useHTML@ qu.3.3.algorithm=\$a=range(2,8); \$c=range(2,8); \$j=range(2,8); \$n=range(2,8); \$b=range(-9,9); \$d=range(-9,9); condition:not(eq(\$b*\$d,0)); \$answer=(\$a*\$n*x^(\$n-1)+\$b)*(\$c*x^(-\$j)+\$d)-\$c*\$j*x^(-\$j-1)*(\$a*x^\$n+\$b*\$x);@ qu.3.3.question=Find the derivative of \${mathml((\$a*x^\$n+\$b*x)*(\$c*x^(-\$j)+\$d))}.@ qu.3.3.answer=\$answer@ qu.3.4.mode=Formula@ qu.3.4.comment=The answer is \${mathml(\$answer)}.@ qu.3.4.editing=useHTML@ qu.3.4.algorithm=\$a=range(1,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,5); \$answer=\$a*\$n*x^(\$n-1)*f+(\$a*x^\$n+\$b)*g;@ qu.3.4.question=Suppose \${mathml(f)} is a function of \${mathml(x)}, with ${f}^{\prime }=g$.
What is the derivative of \${mathml((\$a*x^\$n+\$b)*f)}?@ qu.3.4.answer=\$answer@ qu.4.topic=4-quotient rule@ qu.4.1.mode=Formula@ qu.4.1.comment=Look up the quotient rule! Use \$f for "f", \$g for "g", \$k for "f'" and \$h for "g'".@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=\$f=switch(rint(2),"u","v"); \$k=switch(rint(2),"w","p"); \$g=switch(rint(2),"y","z"); \$h=switch(rint(3),"q","r","s"); \$answer=(\$k*\$g-\$f*\$h)/\$g^2;@ qu.4.1.question=Suppose \${mathml(\$f)} and \${mathml(\$g)} are functions of \${mathml(x)}, with ${\mathrm{f}}^{\prime }=\mathrm{k}$ and ${\mathrm{g}}^{\prime }=\mathrm{h}$. What is the derivative of \${mathml(\$f/\$g)}?@ 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=\$p=range(2,4); \$q=range(2,4); \$a=range(2,4); \$b=range(-10,10); \$c=range(-10,10); condition:lt(\$b*\$c,0); \$num=(\$a*\$p*x^(\$p-1))*(x^\$q+\$c*x)-(\$a*x^\$p+\$b)*(\$q*x^(\$q-1)+\$c); \$denom=(x^\$q+\$c*x)^2; \$answer=(\$num)/\$denom;@ qu.4.2.question=Find the derivative of \${mathml((\$a*x^\$p+\$b)/(x^\$q+\$c*x))}.@ qu.4.2.answer=\$answer@ qu.4.3.mode=Formula@ qu.4.3.comment=The answer is \$answer.@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=\$p=range(2,4); \$q=range(2,4); \$a=range(2,4); \$b=range(-10,10); \$c=range(1,10); condition:not(eq(\$b,0)); \$answer="\$b/\$c";@ qu.4.3.question=Find the derivative of \${mathml((\$a*x^\$p+\$b*x)/(x^\$q+\$c))} at $x=0$.@ qu.4.3.answer=\$answer@ qu.5.topic=5-products with trig functions@ qu.5.1.mode=Formula@ qu.5.1.comment=The answer is \${mathml(\$answer)}.@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=\$p=range(2,4); \$b=range(-9,9); condition:not(eq(\$b,0)); \$var=switch(rint(2),"x","t"); \$r=rint(2); \$fnc=switch(\$r,"cos(\$var)","sin(\$var)"); \$deriv=switch(\$r,"-sin(\$var)","cos(\$var)"); \$answer=\$p*\$var^(\$p-1)*\$fnc+(\$var^\$p+\$b)*\$deriv;@ qu.5.1.question=Find the derivative of \${mathml((\$var^\$p+\$b)*\$fnc)}.@ 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=\$a=range(2,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$r=rint(2); \$answer=\$a*tan(x)+(\$a*x+\$b)*(sec(x))^2;@ qu.5.2.question=Find the derivative of \${mathml((\$a*x+\$b)*tan(x))}.@ qu.5.2.answer=\$answer@ qu.5.3.mode=Formula@ qu.5.3.comment=The answer is \${mathml(\$answer)}.@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=\$a=range(-9,9); \$b=range(-9,9); \$n=range(2,5); condition:not(eq(\$a*\$b,0)); \$r=rint(2); \$fnc=switch(\$r,"cos(x)","sin(x)"); \$deriv=switch(\$r,"-sin(x)","cos(x)"); \$answer=(\$n*x^(\$n-1)+\$a)*(\$b+\$fnc)+(x^\$n+\$a*x)*\$deriv;@ qu.5.3.question=Find the derivative of \${mathml((x^\$n+\$a*x)*(\$b+\$fnc))}.@ qu.5.3.answer=\$answer@ qu.6.topic=6-quotients with trig functions@ qu.6.1.mode=Formula@ qu.6.1.comment=The answer is \${mathml(\$answer)}.@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=\$a=range(1,9); \$b=range(-9,9); \$c=range(1,9); condition:not(eq(\$b,0)); \$p=range(1,6); \$q=range(-6,-1); \$r=rint(3); \$fnc=switch(\$r,"cos(x)","sin(x)","tan(x)"); \$deriv=switch(\$r,"-sin(x)","cos(x)","sec(x)^2"); \$num=(\$a*x^\$p+\$b+\$c*x^\$q)*\$deriv-(\$a*\$p*x^(\$p-1)+\$c*\$q*x^(\$q-1))*\$fnc; \$denom=(\$a*x^\$p+\$b+\$c*x^\$q)^2; \$answer=(\$num)/\$denom;@ qu.6.1.question=Find the derivative of \${mathml(\$fnc/(\$a*x^\$p+\$b+\$c*x^\$q))}.@ 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=\$p=range(2,9); \$b=range(-9,9); \$c=range(-4,4); condition:not(eq(\$b*\$c,0)); \$r=rint(3); \$fnc=switch(\$r,"cos(x)","sin(x)","tan(x)"); \$deriv=switch(\$r,"-sin(x)","cos(x)","sec(x)^2"); \$num=(\$p*x^(\$p-1)+\$b)*(\$fnc+2*\$c*sqrt(x))-(x^\$p+\$b*x)*(\$deriv+\$c*x^(-1/2)); \$denom=(\$fnc+2*\$c*sqrt(x))^2; \$answer=(\$num)/\$denom;@ qu.6.2.question=Find the derivative of \${mathml((x^\$p+\$b*x)/(\$fnc+2*\$c*sqrt(x)))}.@ 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=\$a=range(-9,9); \$b=range(1,9); \$c=range(-9,9); \$d=range(1,9); condition:not(eq(\$a*\$c,0)); \$var=switch(rint(2),"x","t"); \$r=rint(2); \$W=switch(\$r,1,-1); \$fncone=switch(\$r,"cos(\$var)","sin(\$var)"); \$derivone=switch(\$r,"-sin(\$var)","cos(\$var)"); \$fnctwo=switch(\$r,"sin(\$var)","cos(\$var)"); \$derivtwo=switch(\$r,"cos(\$var)","-sin(\$var)"); \$num=\$b*\$c*\$derivone-\$a*\$d*\$derivtwo-\$b*\$d*\$W; \$denom=(\$c+\$d*\$fnctwo)^2; \$answer=(\$num)/\$denom;@ qu.6.3.question=Find the derivative of \${mathml((\$a+\$b*\$fncone)/(\$c+\$d*\$fnctwo))}.@ qu.6.3.answer=\$answer@ qu.7.topic=7-products with exp and ln functions@ qu.7.1.mode=Formula@ qu.7.1.comment=The answer is \${mathml((\$a*\$p*\$var^(\$p-1)+\$b*\$q*\$var^(\$q-1))*("e"^\$var+\$c*\$var^("\$m"/"\$n"))+(\$a*\$var^\$p+\$b*\$var^\$q)*("e"^\$var+("\$c*\$m"/"\$n")*\$var^("\$k"/"\$n")))}.@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=\$p=range(2,6); \$q=range(-6,-1); \$k=range(1,5); \$n=range(2,5); condition:not(eq(\$k,\$n)); condition:not(eq(\$k,2*\$n)); \$m=\$k+\$n; \$a=range(1,9); \$b=range(-9,9); \$c=range(-9,9); condition:not(eq(\$b*\$c,0)); \$var=switch(rint(7),"t","u","v","w","x","y","z"); \$answer=(\$a*\$p*\$var^(\$p-1)+\$b*\$q*\$var^(\$q-1))*("e"^\$var+\$c*\$var^("\$m"/"\$n"))+(\$a*\$var^\$p+\$b*\$var^\$q)*("e"^\$var+(\$c*\$m/\$n)*\$var^("\$k"/"\$n"));@ qu.7.1.question=Find the derivative of \${mathml((\$a*\$var^\$p+\$b*\$var^\$q)*("e"^\$var+\$c*\$var^("\$m"/"\$n")))}.@ 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=\$q=range(2,4); \$p=\$q+range(1,3); \$n=range(2,5); \$a=range(1,9); \$b=range(-9,9); \$c=range(-9,9); condition:not(eq(\$b*\$c,0)); \$answer=(\$a*\$p*x^(\$p-1)+\$b*\$q*x^(\$q-1))*(ln(x)+\$c*x^\$n)+(\$a*x^\$p+\$b*x^\$q)*(1/x+(\$c*\$n)*x^(\$n-1));@ qu.7.2.question=Find the derivative of \${mathml((\$a*x^\$p+\$b*x^\$q)*(ln(x)+\$c*x^\$n))}.@ qu.7.2.answer=\$answer@ qu.7.3.mode=Formula@ qu.7.3.comment=The answer is \${mathml(\$a*\$p*x^(\$p-1)*\$n^x+ln("\$n")*(\$a*x^\$p+\$b)*\$n^x)}.@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=\$p=range(2,6); \$n=range(2,5); \$a=range(1,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$answer=\$a*\$p*x^(\$p-1)*\$n^x+(\$a*x^\$p+\$b)*ln(\$n)*\$n^x;@ qu.7.3.question=Find the derivative of \${mathml((\$a*x^\$p+\$b)*\$n^x)}.@ qu.7.3.answer=\$answer@ qu.8.topic=8-quotients with exp and ln functions@ qu.8.1.mode=Formula@ qu.8.1.comment=The answer is \${mathml( ((1/\$var)*(\$c*\$var^\$n+\$d*"e"^\$var)-(\$c*\$n*\$var^(\$n-1)+\$d*"e"^\$var)*(ln(\$var)))/(\$c*\$var^\$n+\$d*"e"^\$var)^2 )}.@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=\$c=range(1,9); \$d=range(1,9); \$n=range(2,5); \$var=switch(rint(2),"x","t"); \$answer=((1/\$var)*(\$c*\$var^\$n+\$d*"e"^\$var)-(\$c*\$n*\$var^(\$n-1)+\$d*"e"^\$var)*(ln(\$var)))/(\$c*\$var^\$n+\$d*"e"^\$var)^2;@ qu.8.1.question=Find the derivative of \${mathml(ln(\$var)/(\$c*\$var^\$n+\$d*"e"^\$var))}.@ qu.8.1.answer=\$answer@ qu.8.2.mode=Formula@ qu.8.2.comment=The answer is \${mathml( ("e"^x*(\$c*x^\$n+\$d*ln(x)-\$n*\$c*x^(\$n-1)-\$d/x))/(\$c*x^\$n+\$d*ln(x))^2 )}.@ qu.8.2.editing=useHTML@ qu.8.2.algorithm=\$c=range(1,9); \$d=range(1,9); \$n=range(2,5); \$answer= "e"^x*(\$c*x^\$n+\$d*ln(x)-\$n*\$c*x^(\$n-1)-\$d/x)/(\$c*x^\$n+\$d*ln(x))^2;@ qu.8.2.question=Find the derivative of \${mathml("e"^x/(\$c*x^\$n+\$d*ln(x)))}.@ qu.8.2.answer=\$answer@ qu.9.topic=9-chain rule@ qu.9.1.mode=Formula@ qu.9.1.comment=The answer is \${mathml( \$answer )}.@ qu.9.1.editing=useHTML@ qu.9.1.algorithm=\$a=range(2,8); \$b=range(2,8); \$n=range(2,4); \$m=range(4,8); \$answer=\$a*\$m*\$n*x^(\$n-1)*(\$a*x^\$n-\$b)^(\$m-1);@ qu.9.1.question=Find the derivative of \${mathml( (\$a*x^\$n-\$b)^\$m )}.@ 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=\$a=range(1,6); \$b=range(-6,6); \$c=range(1,6); condition:not(eq(\$a*\$b*\$c,0)); \$answer=(\$a*x+\$b)/sqrt(\$a*x^2+2*\$b*x+\$c);@ qu.9.2.question=Find the derivative of \${mathml( sqrt(\$a*x^2+2*\$b*x+\$c) )}.@ qu.9.2.answer=\$answer@ qu.10.topic=10-chain rule with trig functions@ 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(-9,9); condition:not(eq(\$b,0)); \$n=range(2,5); \$arg=\$a*x^\$n+\$b; \$r=rint(3); \$fnc=switch(\$r,"cos(\$arg)","sin(\$arg)","tan(\$arg)","sec(\$arg)"); \$deriv=switch(\$r,"-sin(\$arg)","cos(\$arg)","sec(\$arg)^2","tan(\$arg)*sec(\$arg)"); \$answer=\$a*\$n*x^(\$n-1)*\$deriv;@ qu.10.1.question=Find the derivative of \${mathml( \$fnc )}.@ 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=\$m=range(2,5); \$n=range(2,5); \$a=range(2,6); \$b=range(2,6); \$r=rint(2); \$s=rint(2); \$fncone=switch(\$r,cos(x),sin(x)); \$derivone=switch(\$r,-sin(x),cos(x)); \$answer=\$a*\$m*\$fncone^(\$m-1)*\$derivone;@ qu.10.2.question=Find the derivative of \${mathml( \$a*\$fncone^\$m )}.
Note: to get "cosine squared of \${mathml(x)}", type "(cos x)^2".@ 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=\$b=range(2,6); \$r=rint(2); \$fnc=switch(\$r,cos(x),sin(x)); \$deriv=switch(\$r,-sin(x),cos(x)); \$answer=(\$b+\$deriv)/(2*sqrt(\$b*x+\$fnc));@ qu.10.3.question=Find the derivative of \${mathml( sqrt(\$b*x+\$fnc) )}.@ qu.10.3.answer=\$answer@ qu.11.topic=11-chain rule with exp and ln@ qu.11.1.mode=Formula@ qu.11.1.comment=The answer is \${mathml(\$a*"e"^(\$a*\$x))}.@ qu.11.1.editing=useHTML@ qu.11.1.algorithm=\$a=range(-9,-1); \$x=switch(rint(7),"x","y","z","t","u","v","w"); \$answer=\$a*"e"^(\$a*\$x);@ qu.11.1.question=Find the derivative of \${mathml("e"^(\$a*\$x))}.

Note that exponents should be entered with parentheses; for example, type "e^(3x)" rather than "e^3x".@ qu.11.1.answer=\$answer@ qu.11.2.mode=Formula@ qu.11.2.comment=The answer is \${mathml(\$answer)}.@ qu.11.2.editing=useHTML@ qu.11.2.algorithm=\$a=range(1,9); \$b=range(-9,9); condition:not(eq(\$b,0)); \$n=range(2,5); \$answer=(\$a*\$n*x^(\$n-1))/(\$a*x^\$n+\$b);@ qu.11.2.question=Find the derivative of \${mathml(ln(\$a*x^\$n+\$b))}.@ qu.11.2.answer=\$answer@ qu.11.3.mode=Formula@ qu.11.3.comment=The answer is \${mathml( \$n*(\$b*x+"e"^(-\$a*x))^(\$n-1)*(\$b-\$a*"e"^(-\$a*x)) )}.@ qu.11.3.editing=useHTML@ qu.11.3.algorithm=\$a=range(1,9); \$b=range(1,9); \$n=range(2,5); \$answer=\$n*(\$b*x+"e"^(-\$a*x))^(\$n-1)*(\$b-\$a*"e"^(-\$a*x));@ qu.11.3.question=Find the derivative of \${mathml((\$b*x+"e"^(-\$a*\$x))^\$n)}.
Note: to get "cosine squared of [\${mathml(x^2+1)}]", type "cos (x^2+1)^2".@ qu.12.1.answer=\$answer@ qu.12.2.mode=Formula@ qu.12.2.comment=The answer is \${mathml(\$answer)}.@ qu.12.2.editing=useHTML@ qu.12.2.algorithm=\$a=range(1,9); \$b=range(1,9); \$arg=\$x^2+\$b*x+\$a; \$argprime=2*\$x+\$b; \$r=rint(2); \$fnc=switch(\$r,cos(\$arg),sin(\$arg)); \$fac=switch(\$r,-(\$argprime),(\$argprime)); \$answer=switch(\$r,-(\$argprime)*tan(\$arg),(\$argprime)*cot(\$arg));@ qu.12.2.question=Find the derivative of \${mathml( ln(\$fnc) )}.@ qu.12.2.answer=\$answer@ qu.12.3.mode=Formula@ qu.12.3.comment=The answer is \${mathml(\$sign*\$a*\$n*x^(\$n-1))} ${e}^{\mathrm{a}{x}^{\mathrm{n}}}\mathrm{other}\left({e}^{\mathrm{a}{x}^{\mathrm{n}}}\right)$.@ qu.12.3.editing=useHTML@ qu.12.3.algorithm=\$a=range(2,6); \$n=range(2,5); \$arg=\$a*x^\$n; \$r=rint(2); \$fnc=switch(\$r,"sin","cos"); \$other=switch(\$r,"cos","sin"); \$sign=switch(\$r,1,-1); \$answer=\$sign*\$a*\$n*x^(\$n-1)*"e"^(\$arg)*\$other("e"^(\$arg));@ qu.12.3.question=Find the derivative of $\mathrm{fnc}\left({e}^{\mathrm{a}{x}^{\mathrm{n}}}\right)$.
Note that exponents should be entered with parentheses; for example, type "e^(3x)" rather than "e^3x".@ qu.12.3.answer=\$answer@ qu.12.4.mode=Formula@ qu.12.4.comment=The answer is \${mathml(\$answer)}.@ qu.12.4.editing=useHTML@ qu.12.4.algorithm=\$a=range(1,2); \$b=range(-9,9,2); \$n=range(2,5); \$arg=sqrt(2*\$a*x^\$n+\$b); \$r=rint(2); \$fnc=switch(\$r,"cos(\$arg)","sin(\$arg)"); \$deriv=switch(\$r,"-sin(\$arg)","cos(\$arg)"); \$answer=((\$a*\$n*x^(\$n-1))/\$arg)*\$deriv;@ qu.12.4.question=Find the derivative of \${mathml( \$fnc )}.@ qu.12.4.answer=\$answer@ qu.13.topic=13chain rule with product rule@ qu.13.1.mode=Formula@ qu.13.1.comment=The answer is $\left($ \${mathml(\$poly)} $\right){e}^{{\mathrm{a}x}^{\mathrm{n}}}$.@ qu.13.1.editing=useHTML@ qu.13.1.algorithm=\$m=range(2,5); \$n=range(2,5); \$a=range(-6,6); condition:not(eq(\$a*(\$a-1)*(\$a+1),0)); \$poly=\$m*x^(\$m-1)+\$a*\$n*x^(\$n+\$m-1); \$answer=(\$poly)*"e"^(\$a*x^\$n);@ qu.13.1.question=Find the derivative of \${mathml(x^\$m)} ${e}^{{\mathrm{a}x}^{\mathrm{n}}}$.