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Popular >

derivative of \sqrt[3]{x+sqrt(x)}

Solution

Solution

\frac{2 x + 1}{6 x ( x + x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( x + x ) ^{\frac{2}{3}}} \frac{d}{d x} (x + x)

= \frac{1}{3 ( x + x ) ^{\frac{2}{3}}} \frac{d}{d x} (x + x)

\frac{d}{d x} (x + x) = 1 + \frac{1}{2 x}

= \frac{1}{3 ( x + x ) ^{\frac{2}{3}}} (1 + \frac{1}{2 x})

Simplify

\frac{1}{3 ( x + x ) ^{\frac{2}{3}}} (1 + \frac{1}{2 x}) : \frac{2 x + 1}{6 x ( x + x ) ^{\frac{2}{3}}}

= \frac{2 x + 1}{6 x ( x + x ) ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x+sqrt(x)} ?
The derivative of \sqrt[3]{x+sqrt(x)} is (2sqrt(x)+1)/(6sqrt(x)(x+\sqrt{x))^{2/3}}
What is the first derivative of \sqrt[3]{x+sqrt(x)} ?
The first derivative of \sqrt[3]{x+sqrt(x)} is (2sqrt(x)+1)/(6sqrt(x)(x+\sqrt{x))^{2/3}}