# Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\cot ^{2} x$

Solution:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u \cdot v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Formula used: $\frac{d}{d x}\left(\cot ^{a} n u\right)=\operatorname{acot}^{a-1}(n u) \times \frac{d}{d x}(\cot n u) \times \frac{d}{d x}(n u)$ and $\frac{d x^{n}}{d x}=n x^{n-1}$

Let us take $y=\cot ^{2} x$

So, by using the above formula, we have

$\frac{d}{d x} \cot ^{2} x=2 \cot (x) \times \frac{d \cot x}{d x} \times \frac{d x}{d x}=-2 \cot x\left(\operatorname{cosec}^{2} x\right)$

Differentiation of $y=\cot ^{2} x$ is $-2 \cot x\left(\operatorname{cosec}^{2} x\right)$