Question

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

Answer 1

let y = $\frac {e^x}{sin\ x}$
By using the quotient rule, we obtain

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

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

$\frac {dy}{dx}$ = $\frac {e^x(sin\ x-cos\ x)}{sin^2x}$, x ≠ n$\pi$, n∈Z