Question

If $y=\log \left(\sin x\right),$ find $\frac{dy}{dx}$.

Answer 1

Given that $y=\log \left(\sin x\right)$, we need to find the value of $\frac{dy}{dx}$

We know that the derivative of $\log \left(x\right)$ w.r.t $x$ is $\frac{1}{x}$

$⟹\frac{dy}{dx}=\frac{d}{dx}\left(\log \right(\sin x\left)\right)=\frac{1}{\sin x}\times \frac{d}{dx}\left(\sin x\right)=\frac{1}{\sin x}\times \cos x=\cot x$

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