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Popular >

derivative of (x^2^{1/3})

Solution

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

Solution

\frac{2}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

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

= \frac{2}{3 x ^{\frac{1}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2^{1/3}) ?
The derivative of (x^2^{1/3}) is 2/(3x^{1/3)}
What is the first derivative of (x^2^{1/3}) ?
The first derivative of (x^2^{1/3}) is 2/(3x^{1/3)}