Question

Differentiate the following w.r.t $x$: $\frac{e^x}{\sin x}$

Answer 1

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

$=\frac{e^x\sin x-e^x\cos x}{{\sin }^{x}x}$

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