Question

If $y=\log \left(\sin x\right)$ then find $\frac{d^{2}y}{d{x}^2}$

Answer 1

Differentiating $y=\log \left(\sin x\right)$ with respect to $x$,

$\frac{dy}{dx}=\frac{\cos x}{\sin x}$

$\frac{dy}{dx}=\cot x$

Again differentiating with respect to $x$,

$\frac{d^{2}y}{d{x}^2}=-{\csc }^{2}x$