Question

Find the derivatives of the following:
(i) ${\cot }^{n}x$
(ii) $\tan \left(e^x\right)$

Answer 1

ii) $\frac{d}{dx}{\cot }^{n}x=n{\cot }^{n-1}x\cdot (-cose{c}^{2}x)$

$=-n{\cot }^{n-1}x\cdot cose{c}^{2}x$

ii) $\frac{d}{dx}\tan \left(e^x\right)={\sec }^2\left(e^x\right)\cdot e^x$.