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Find the derivative of f(x)\, with respect to x\,: f(x)=x\sin x\,

This is a product of two functions. If you know how to take the derivative of the functions separately, the product rule tells us how to take the derivative of their product.

f'(x)=x{\frac  {d}{dx}}(\sin x)+{\frac  {d}{dx}}(x)(\sin x)\,

f'(x)=x\cos x+\sin x\,

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