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Compute the derivative of the given function

Compute the derivative of the function

    \[ f(x) = \sin (\cos^2 x) \cdot \cos (\sin^2 x). \]


Using the chain rule we compute,

    \begin{align*}  f'(x) &= \cos (\cos^2 x)(-2 \cos x \sin x)\cos (\sin^2 x) + \sin (\cos^2 x)(-\sin (\sin^2 x))2 \sin x \cos x \\   &= (-2 \sin x \cos x)(\cos (\cos^2 x)\cos (\sin^2 x) + \sin (\cos^2 x)\sin (\sin^2 x)) \\  &= -\sin (2x) (\cos (\cos^2 x - \sin^2 x)) \\  &= - \sin (2x) \cdot \cos(\cos (2x)). \end{align*}

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