`f(x) = sqrt(x) - 6root(3)(x)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.2 - Problem 49 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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Rewrite the function with exponents.

`f(x) = x^(1/2)-6x^(1/3)`

Use the power rule to solve.

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

Simplify and eliminate the negative fractions by writing them as a fraction.

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

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