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AP® Calculus AB-BC

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Moderate

Derivative of Sum of Two Power Functions: Radicals

APCALC-C44XXW

Given $f(x)=\sqrt[3]{x}+\cfrac{1}{x\sqrt{x}}$, find $f’(x)$.

A

$f’(x)=\cfrac{1}{3\sqrt{x^3}}-\cfrac{3}{2\sqrt[5]{x^2}}$

B

$f’(x)=\cfrac{1}{3\sqrt[3]{x^2}}-\cfrac{3}{2\sqrt{x^5}}$

C

$f’(x)=\cfrac{1}{3\sqrt[3]{x^2}}-\cfrac{3}{2\sqrt{x}}$

D

$f’(x)=\cfrac{3}{\sqrt[3]{x^2}}-\cfrac{2}{3\sqrt{x}}$