Differentiate the following with respect to x:

To Find: Differentiation

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

$\frac{\mathrm{d}(\mathrm{u} \cdot \mathrm{v})}{\mathrm{dx}}=\mathrm{V} \frac{\mathrm{du}}{\mathrm{dx}}+\mathrm{u} \frac{\mathrm{dv}}{\mathrm{dx}}$

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

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

So, by using the above formula, we have

$\frac{d}{d x} e^{\cot x}=e^{\cot x} \times \frac{d \cot x}{d x}=-e^{\cot x} \operatorname{cosec}^{2} x$

Differentiation of $y=e^{\cot x}$ is $-e^{\cot x} \operatorname{cosec}^{2} x$