Question

Differentiate the following questions w.r.t. x.

$\frac{e^x}{sinx}$

Answer 1

Let y = $\frac{e^x}{sinx}$. Differenatiate both sides w.r.t. x, we get

$\frac{dy}{dx}=\frac{d}{dx}\left(\frac{e^x}{sinx}\right)[UsingQuotientrule\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\frac{d}{dx}u-u\frac{d}{dx}v}{v^2}]$

$=\frac{sinx\frac{d}{dx}{e}^x-e^x\frac{d}{dx}sinx}{si{n}^{2}x}=\frac{sinx{e}^x-e^{x}cosx}{si{n}^{2}x}=\frac{e^x(sinx-cosx)}{si{n}^{2}x},x\ne n\pi ,nϵZ.$