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Popular >

derivative of (9-x^2^{2/3})

Solution

\frac{d}{d x} ((9 - x^{2})^{\frac{2}{3}})

Solution

- \frac{4 x}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((9 - x^{2})^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}} \frac{d}{d x} (9 - x^{2})

= \frac{2}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - 2 x

= \frac{2}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}} (- 2 x)

Simplify

\frac{2}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}} (- 2 x) : - \frac{4 x}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}}

= - \frac{4 x}{3 ( 9 - x ^{2} ) ^{\frac{1}{3}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (9-x^2^{2/3}) ?
The derivative of (9-x^2^{2/3}) is -(4x)/(3(9-x^2)^{1/3)}
What is the first derivative of (9-x^2^{2/3}) ?
The first derivative of (9-x^2^{2/3}) is -(4x)/(3(9-x^2)^{1/3)}