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Q.

The derivative of $\sin^{2} x$ with respect to ${(\log x)}^{2}$ is

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An Intiative by Sri Chaitanya

a

$\frac{x \sin x \cos x}{{(\log x)}^{2}}$

b

$\frac{\sin^{2} x}{2 \log x}$

c

$\frac{x \sin x \cos x}{\log x}$

d

$x \log x$

answer is A.

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Detailed Solution

Let $y = \sin^{2} x$

$\frac{d y}{d x} = 2 \sin x . \cos x$

$u = {(\log x)}^{2} \Rightarrow \frac{d u}{d x} = \frac{2 \log x}{x}$

$\frac{d y}{d u} = \frac{2 \sin x . \cos x}{2 \log x} . x$

$\frac{d y}{d u} = \frac{x \sin x . \cos x}{\log x}$

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