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

(A) $\tan x$

(B) $\cot x$

(C) $f(\cos x)$

(D) $\frac{1}{x}$

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Best answer

SOLUTION —

We have,

$\begin{array}{rlrl}\Rightarrow & y & =\log (\sin x) \\\therefore & \frac{d y}{d x} & =\frac{1}{\sin x} \times \cos x \\& =\cot x\end{array}$

So, The correct option will be (B).

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