`f(x) = (root(3)(x))(sqrt(x) + 3)` Find the derivative of the algebraic function.

Textbook Question

Chapter 2, 2.3 - Problem 30 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`f(x) = x^(1/3)(sqrt(x) + 3)`

`or, f(x) = x^(1/3)(x^(1/2) + 3)`

`or, f(x) = x^(5/6) + 3x^(1/3)`

`f'(x) = (5/6)x^(-1/6) + 3*(1/3)x^(-2/3)`

`or, f'(x) = (5/6)*x^(-1/6) + x^(-2/3)`

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