Question

Differentiate the following w.r.t. x: log(cos ex)

Answer 1

Let y=log(cos ex)

By using the chain rule, we obtain

$\frac{dy}{dx}=\frac{d}{dx}[log(cos e^x]$

=$\frac{1}{cose^x}.\frac{d}{dx}(cose^x)$

=$\frac{1}{cose^x}.(-sin e^x).\frac{d}{dx}(e^x)$

=$\frac{-sin e^x}{cos e^x}.e^x$

=-$e^x tan e^x,e^x$≠(2n+1)\frac{\pi}{2},$$nεN