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 and . 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 .
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 and . 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 .@
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))^$n)}.
Note that exponents should be entered with parentheses; for example, type "e^(3x)" rather than "e^3x".@
qu.11.3.answer=$answer@
qu.11.4.mode=Formula@
qu.11.4.comment=The answer is ${mathml($answer)}.@
qu.11.4.editing=useHTML@
qu.11.4.algorithm=$n=range(2,15);
$answer=($n*(ln(x))^($n-1))/x;@
qu.11.4.question=Find the derivative of ${mathml((ln(x)^$n))}.@
qu.11.4.answer=$answer@
qu.12.topic=12-repeated chain rule@
qu.12.1.mode=Formula@
qu.12.1.comment=The answer is ${mathml($answer)}.@
qu.12.1.editing=useHTML@
qu.12.1.algorithm=$m=range(2,5);
$n=range(2,5);
$a=range(2,6);
$b=range(2,6);
$arg=$a*x^$n+$b;
$r=rint(2);
$fnc=switch($r,cos($arg),sin($arg));
$deriv=switch($r,-sin($arg),cos($arg));
$answer=$a*$m*$n*x^($n-1)*$fnc^($m-1)*$deriv;@
qu.12.1.question=Find the derivative of ${mathml( $fnc^$m )}.
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^($n-1))}
.@
qu.12.3.editing=useHTML@
qu.12.3.algorithm=$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
.
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
${mathml($poly)}
.@
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)}
.
Note that exponents should be entered with parentheses;
for example, type "e^(3x)" rather than "e^3x".@
qu.13.1.answer=$answer@
qu.13.2.mode=Formula@
qu.13.2.comment=The answer is ${mathml($sign*($poly)*"e"^($a*x)*$other(x^$n*"e"^($a*x)))}.@
qu.13.2.editing=useHTML@
qu.13.2.algorithm=$n=range(2,6);
$a=range(-6,6);
condition:not(eq($a*($a-1)*($a+1),0));
$r=rint(2);$fnc=switch($r,"sin","cos");
$other=switch($r,"cos","sin");
$sign=switch($r,1,-1);
$poly=$n*x^($n-1)+$a*x^$n;
$answer=$sign*($poly)*"e"^($a*x)*$other(x^$n*"e"^($a*x));@
qu.13.2.question=Find the derivative of ${mathml($fnc(x^$n*"e"^($a*x)))}.
Note that exponents should be entered with parentheses;
for example, type "e^(3x)" rather than "e^3x".@
qu.13.2.answer=$answer@
qu.13.3.mode=Formula@
qu.13.3.comment=This problem is easier to do by the product rule than the quotient rule. The answer is ${mathml(-$a*"e"^(-$a*x)*($poly)^(-$n)-$m*$n*x^($m-1)*($poly)^(-$n-1)*"e"^(-$a*x))}.@
qu.13.3.editing=useHTML@
qu.13.3.algorithm=$m=range(2,5);
$n=range(2,5);
$a=range(1,6);
$c=range(-9,9);
condition:not(eq($c,0));
$poly=x^$m+$c;
$answer=-$a*"e"^(-$a*x)*($poly)^(-$n)-$m*$n*x^($m-1)*($poly)^(-$n-1)*"e"^(-$a*x);@
qu.13.3.question=Find the derivative of ${mathml( ("e"^(-$a*x))/(x^$m+$c)^$n )}.
Note that exponents should be entered with parentheses; for example, type "e^(3x)" rather than "e^3x".@
qu.13.3.answer=$answer@
qu.13.4.mode=Formula@
qu.13.4.comment=The answer is ${mathml("$answer")}.@
qu.13.4.editing=useHTML@
qu.13.4.algorithm=$a=range(2,6);
$n=range(2,6);
$b=range(2,6);
$r=rint(2);
$fnc=switch($r,cos(x),sin(x));
$deriv=switch($r,-sin(x),cos(x));
$f=x^$n*"e"^(-$a*x)+$b*$fnc;
$answer=(($n*x^($n-1)-$a*x^$n)*"e"^(-$a*x)+$b*($deriv))/("$f");@
qu.13.4.question=Find the derivative of ${mathml( ln("$f") )}.@
qu.13.4.answer=$answer@
qu.14.topic=14-implicit differentiation@
qu.14.1.mode=Formula@
qu.14.1.comment=The answer is ${mathml("$num/$den"*x^($m-1)/y^($n-1))}.@
qu.14.1.editing=useHTML@
qu.14.1.algorithm=$m=range(-5,5);
$n=range(2,5);
$a=range(-9,9);
$b=range(2,9);
$c=range(2,9);
condition:not(eq($a*$m*($m-1),0));
$num=-$b*$m;
$den=$n*$c;
$answer=($num/$den)*x^($m-1)/(y^($n-1));@
qu.14.1.question=Find ${mathml((dy)/(dx))} if ${mathml($b*x^$m+$c*y^$n)}= ${mathml($a*"pi")}.@
qu.14.1.answer=$answer@
qu.14.2.mode=Formula@
qu.14.2.comment=The answer is ${mathml($answer)}.@
qu.14.2.editing=useHTML@
qu.14.2.algorithm=$m=range(2,6);
$n=range(2,6);
$p=range(2,6);
$q=range(2,6);
$a=range(2,9);
condition:not(eq($a,0));
$num=$m*x^($m-1)*y^$n+$p*x^($p-1);
$den=$a*$q*y^($q-1)-$n*x^$m*y^($n-1);
$answer=($num)/($den);@
qu.14.2.question=Find ${mathml((dy)/(dx))} if ${mathml(x^$m*y^$n+x^$p)}= ${mathml($a*y^$q)}.@
qu.14.2.answer=$answer@