`h(x) = 6sqrt(x) + 3root(3)(x)` Use the rules of differentiation to find the derivative of the function.

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Chapter 2, Review - Problem 13 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `h(x)=6sqrt(x)+3root(3)(x)`

Rewrite the function as `h(x)=6x^(1/2)+3x^(1/3)`

To find the derivative, use the power rule for derivatives.

`h'(x)=(1/2)6x^(-1/2)+(1/3)3x^(-2/3)`

`h'(x)=3x^(-1/2)+x^(-2/3)`

`h'(x)=3/(x^(1/2))+1/x^(2/3)`

`h'(x)=(3)/(sqrt(x))+1/root(3)(x^2)`

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