Calc2.22

From Exampleproblems

Find the derivative of $f(x)\,$ with respect to $x\,$ : $f(x)=\ln (\sin (e^x))\,$

Here, we must use the chain rule inside of the chain rule.

$f'(x)=\frac{1}{\sin (e^x)}\frac{d}{dx}\sin e^x=\frac{1}{\sin (e^x)}\cos (e^x)\frac{d}{dx}e^x=\frac{1}{\sin (e^x)}\cos (e^x)(e^x)\,$