Question
Diffrentiate the following w.r.t.x
$\sin ^2 x^2-\cos ^2 x^2$
$\sin ^2 x^2-\cos ^2 x^2$
Differentiating w.r.t. x, we get
$\begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}\left[\sin ^2 x^2-\cos ^2 x^2\right] \\ & =\frac{d}{d x}\left(\sin x^2\right)^2-\frac{d}{d x}\left(\cos x^2\right)^2 \\ & =2 \sin x^2 \cdot \frac{d}{d x}\left(\sin x^2\right)-2 \cos x^2 \cdot \frac{d}{d x}\left(\cos x^2\right) \\ & =2 \sin x^2 \cdot \cos x^2 \cdot \frac{d}{d x}\left(x^2\right)-2 \cos x^2 \cdot\left(-\sin x^2\right) \cdot \frac{d}{d x}\left(x^2\right) \\ & =2 \sin x^2 \cdot \cos x^2 \times 2 x+2 \sin x^2 \cdot \cos x^2 \times 2 x \\ & =4 x\left(2 \sin x^2 \cdot \cos x^2\right) \\ & =4 x \sin \left(2 x^2\right) .\end{aligned}$
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