# How do you differentiate f(x)=(cot(x))^2  using the chain rule?

Jan 23, 2016

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

#### Explanation:

Use the chain rule. The first issue here is the second power. According to the chain rule, $\frac{d}{\mathrm{dx}} \left[{u}^{2}\right] = 2 u \cdot u '$, and here we have $u = \cot \left(x\right)$, giving us

$f ' \left(x\right) = 2 \cot \left(x\right) \cdot \frac{d}{\mathrm{dx}} \left[\cot \left(x\right)\right]$

The derivative of $\cot \left(x\right)$ is $- {\csc}^{2} \left(x\right)$.

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