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Find the derivative of f(x)\, with respect to x\,: f(x)=x^{3}\cos x\,

Use the product rule to find the derivative.

f'(x)=x^{3}{\frac  {d}{dx}}(\cos x)+{\frac  {d}{dx}}(x^{3})(\cos x)\,

f'(x)=x^{3}(-\sin x)+3x^{2}\cos x\,

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