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

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Chapter 2, Review - Problem 31 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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).`

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