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Compute the derivative of the given function

Compute the derivative of the function

    \[ f(x) = (2-x^2)\cos (x^2) + 2x \sin (x^3). \]


Using the chain rule we compute,

    \begin{align*}  f'(x) &= (-2x)\cos (x^2) + (2-x^2)(2x)(-\sin (x^2)) + 2 \sin (x^3) + (2x)(3x^2) \cos (x^3) \\  &= (2x^3 -4x)\sin (x^2) - 2x \cos (x^2) + 2 \sin (x^3) + 6x^3 \cos (x^3). \end{align*}

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