Differentiate with respect to $x$ : ${sin}^{2} (x^{2})$

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Solution

Let $p = s i n^{2} (x^{2})$ on differentiating we get
$\Rightarrow \frac{d p}{d x} = \frac{d}{d x} s i n^{2} (x^{2})$
$\frac{d p}{d x} = 2 s i n (x^{2}) c o s (x^{2}) \times \frac{d}{d x} (x^{2})$
$\frac{d p}{d x} = 4 x s i n (x^{2}) c o s (x^{2})$

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