Question

Differentiate the given function w.r.t. $x$.
$\frac{e^x}{\sin x}$

Answer 1

Let $y=\frac{e^x}{\sin x}$

Thus by using the quotient rule, we obtain

$\frac{dy}{dx}=\frac{\sin x\frac{d}{dx}\left(e^x\right)-e^x\frac{d}{dx}\left(\sin x\right)}{{\sin }^{2}x}$

$=\frac{\sin x.\left(e^x\right)-e^x.\left(\cos x\right)}{{\sin }^{2}x}$

$=\frac{e^x(\sin x-\cos x)}{{\sin }^{2}x},x\ne n\pi ,n\in Z$