Question

Differentiate: $\frac{e^x}{\sin x}$

Answer 1

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

we know that ,if $y=\frac{f\left(x\right)}{g\left(x\right)}$ then $\frac{dy}{dx}=\frac{f^{{}^{\prime }}\left(x\right)g\left(x\right)-g^{{}^{\prime }}\left(x\right)f\left(x\right)}{\left(g\right(x){)}^2}$

$\frac{dy}{dx}=\frac{e^x\sin x-e^x\cos x}{{\sin }^{2}x}$

$\therefore \frac{dy}{dx}=\frac{e^x(\sin x-\cos x)}{si{n}^{2}x}$