Differentiate ${sin}^{2} (x^{2})$ w.r.t. $x^{2}$ .

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Solution

Let f= $s i n^{2} x^{2}; g = x^{2}$
to get $\frac{d f}{d g} = \frac{d f}{d n} \times \frac{d x}{d g} = \frac{d f / d x}{d g / d x} = \frac{2 s i n^{2} . c o s^{2} .2 x}{2 x}$
$= 2 s i n x^{2} c o s x^{2} = s i n (2 x^{2})$

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