Question

Let $y={\log }_e\sin x$ then find $\frac{d^{2}y}{d{x}^2}$

Answer 1

Given,

$y={\log }_e\sin x$

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

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

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

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

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