<s>[INST] If $f’(x) = \sin x + (\sin4x)(\cos x)$, then $f’(2x^2 + \pi/2) $is? If $$f'(x) = \sin x + \sin4x \cdot \cos x,$$ then $$f'(2x^2 + \pi/2)$$ is?
Given answer: $$4x\cos(2x^2) – 4x\sin(8x^2) \sin(2x^2)$$
I tried and I'm getting the answer as $\cos(2x^2) - \sin(8x^2)\sin(2x^2)$
 [/INST] $$f\'(x) = \sin x + \sin 4x \cos x$$
We need to find $f\'(2x^2+\pi/2)$.
Now
$$f\'(2x^2+π/2) = f\'(2x^2+π/2).Derivative of (2x^2+π/2)$$
$$ = {\sin (2x^2+π/2) + \sin 4(2x^2+π/2).Cos(2x^2+π/2)}.4x$$
$$ = 4x{\cos(2x^2) - \sin(8x^2).\sin(2x^2)}$$
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