Question

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

Answer 1

Given, $y=\log \left(\sin x\right)$

Now differentiating both sides with respect to $x$ we get,

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

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

Now again differentiating both sides with respect to $x$ we get,

$\frac{d^{2}y}{d{x}^2}=-cose{c}^{2}x$.