Question

Differential coefficient of $\log \sin x$ is :

• A. $\cos x$
• B. $\tan x$
• C. $\text{cosec}x$
• D. $\cot x$

Answer 1

Answer: (D)

$\cot x$

We have,

$y=\log \sin x$

On differentiating w.r.t $x$, we get

$\frac{dy}{dx}=\frac{d\left(\log \sin x\right)}{dx}$

$\frac{dy}{dx}=\frac{1}{\sin x}\times \cos x$

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

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

Hence, this is the answer.