# What is the derivative of  (cot^(2)x)?

Dec 18, 2015

$- 2 {\csc}^{2} x \cot x$

#### Explanation:

Treat ${\cot}^{2} x$ like ${u}^{2}$, where $u = \cot x$.

According to the chain rule,

$\frac{d}{\mathrm{dx}} \left[{u}^{2}\right] = 2 u \cdot u '$

Therefore,

$\frac{d}{\mathrm{dx}} \left[{\cot}^{2} x\right] = 2 \cot x \cdot \frac{d}{\mathrm{dx}} \left[\cot x\right]$

Know that $\frac{d}{\mathrm{dx}} \left[\cot x\right] = - {\csc}^{2} x$

Thus,

$\frac{d}{\mathrm{dx}} \left[{\cot}^{2} x\right] = - 2 {\csc}^{2} x \cot x$