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Moderate

Derivative of Roots of x

SVCALC-@NHWZQ

Find the derivative of $f(x)=\sqrt{x}(\sqrt[3]{x}+\sqrt[4]{x})$.

A

$\dfrac{1}{2\sqrt{x}}\left(\dfrac{1}{3\sqrt[3]{x}} + \dfrac{1}{4\sqrt[4]{x}}\right)$

B

$\dfrac{1}{2\sqrt{x}}\left(\dfrac{1}{3\sqrt[3]{x^2}} + \dfrac{1}{4\sqrt[4]{x^3}}\right)$

C

$\dfrac{5}{6\sqrt[6]{x}} + \dfrac{3}{4\sqrt[4]{x}}$

D

$\dfrac{1}{6\sqrt[6]{x^5}} + \dfrac{1}{8\sqrt[8]{x^7}}$