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Popular >

derivative of \sqrt[5]{x^3}

Solution

derivative of

Solution

\frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

Solution steps

Apply the chain rule:

\frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{3})

= \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{3})

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

= \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \cdot 3 x^{2}

Simplify

\frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \cdot 3 x^{2} : \frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

= \frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[5]{x^3} ?
The derivative of \sqrt[5]{x^3} is (3x^2)/(5(x^3)^{4/5)}
What is the first derivative of \sqrt[5]{x^3} ?
The first derivative of \sqrt[5]{x^3} is (3x^2)/(5(x^3)^{4/5)}