`h(x) = sqrt(x)sin(x)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that:

`f'(x) = (sqrt x)'(sin x) + (sqrt x)(sin x)'`

`f'(x) = (1/(2sqrt x))(sin x) + (sqrt x)(cos x)`

Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = (1/(2sqrt x))(sin x) + (sqrt x)(cos x).`