Compute the derivative of $f (x) = {sin}^{2} x .$

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Solution

Given : $f (x) = {sin}^{2} x$
$\Rightarrow f (x) = sin x \cdot sin x$
Using product rule
$\Rightarrow f^{'} (x) = (sin x)^{'} \cdot sin x + (sin x)^{'} \cdot sin x$
$\Rightarrow f^{'} (x) = cos x \cdot sin x + cos x \cdot sin x$
$\Rightarrow f^{'} (x) = 2 cos x sin x$
$\Rightarrow f^{'} (x) = sin 2 x$
Hence, $f^{'} (x) = sin 2 x$

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