Question

How do you differentiate `f(x)=cot(e^(x))` using the chain rule?

Answer 1

`f'(x)=-e^x\cosec^2(e^x)`

Explanation:

Given function:

`f(x)=\cot(e^x)`

`\frac{d}{dx}f(x)=frac{d}{dx}(\cot (e^x))`

`f'(x)=-\cosec^2 (e^x)\frac{d}{dx}(e^x)`

`=-\cosec^2 (e^x)(e^x)`

`=-e^x\cosec^2(e^x)`