# What is the second derivative of f(x)=-cot^2x ?

Jun 17, 2018

$f ' ' \left(x\right) = - 4 {\cot}^{2} \left(x\right) {\csc}^{2} \left(x\right) - 2 \csc {x}^{4} \left(x\right)$

#### Explanation:

The first derivative is given by

$f ' \left(x\right) = 2 {\cot}^{2} \left(x\right) \cdot {\csc}^{2} \left(x\right)$
so we get

$f ' ' \left(x\right) = - 4 {\cot}^{2} \left(x\right) {\csc}^{2} \left(x\right) - 2 {\csc}^{4} \left(x\right)$