`g(x) = 3xsin(x) + (x^2)cos(x)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

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sciencesolve eNotes educator| Certified Educator

You need to evaluate the derivative of the given function, using the product tule for the products `3x*sin x ` and  `x^2*cos x` , such that:

`f'(x) = (3x)'*(sin x) + 3x*(sin x)' + (x^2)'(cos x) + (x^2)(cos x)'`

`f'(x) = 3*(sin x)+ 3x*(cos x) + 2x*cos x + x^2*(-sin x)`

Combining like terms yields:

`f'(x) = sin x*(3 - x^2) + x*(cos x)*(3 + 2)`

`f'(x) = sin x*(3 - x^2) + 5x*cos x`

Hence, evaluating the derivative of the function, using the product rule where it is requested, yields` f'(x) = sin x*(3 - x^2) + 5x*cos x.`