`h(x) = sqrt(x)/(x^3 + 1)` Use the Quotient Rule to find the derivative of the function.

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Chapter 2, 2.3 - Problem 9 - 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 find derivative of the function using the quotient rule:

`f'(x)= ((sqrt x)'*(x^3+1) -(sqrt x)*(x^3+1)')/((x^3+1)^2)`

`f'(x)= ((x^3+1)/(2(sqrt x)) -(sqrt x)*(3x^2))/((x^3+1)^2)`

`f'(x)= (x^3+1 -6x^3)/((2sqrt x)*(x^3+1)^2)`

Reducing like terms yields:

` f'(x)= (-5x^3+1)/((2sqrt x)*(x^3+1)^2)` 

Hence, evaluating the derivative of the function, yields `f'(x)= (-5x^3+1)/((2sqrt x)*(x^3+1)^2).`

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