Question

$y=log\left(sinx2\right)$, then find $\frac{dy}{dx}$ = ?

Answer 1

$Y$=$log\left(sin{x}^2\right)$$sin{x}^2=u$

Therefore by applying chain rule,

$\frac{dy}{dx}=\frac{dlogu}{du}\ast \frac{dsin{x}^2}{dx}$

$\frac{dy}{dx}=\frac{1}{u}\ast cos{x}^2=\frac{1}{sin{x}^2}\ast cos{x}^2=cotx$

Therefore,

$\frac{dy}{dx}=cotx$