Differentiate the following equation:
$s i n^{2} x$

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Solution

We have, $= \frac{d}{d x} (s i n^{2} x)$
$= \frac{d}{d x} (s i n x) (s i n x)$
$= s i n x \frac{d}{d x} (s i n x) + s i n x \frac{d}{d x} (s i n x)$ [Using product rule]
$= s i n x \times c o s x + s i n x \times c o s x$
$= 2 s i n x c o s x$
$= s i n 2 x$ $[∵ s i n 2 A = 2 s i n A c o s A]$

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