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Popular >

derivative of \sqrt[5]{2-x^2}

Solution

Solution

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

Solution steps

Apply the chain rule:

\frac{1}{5 ( 2 - x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (2 - x^{2})

= \frac{1}{5 ( 2 - x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (2 - x^{2})

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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