Question

The differential coefficient of $f\left(\sin x\right)$ with respect to $x$ where $f\left(x\right)=\log x$ is:

• A. $\tan x$
• B. $\cot x$
• C. $f\left(\cos x\right)$
• D. $\frac{1}{x}$

Answer 1

The correct option is B $\cot x$

Since $f\left(x\right)=\log x,f\left(\sin x\right)=\log \left(\sin x\right)$
$\frac{df\left(\sin x\right)}{dx}$$=\frac{d\left[\log \right(\sin x\left)\right]}{dx}$

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