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Popular >

derivative of \sqrt[5]{(x^2+x/(x+1)})

Solution

Solution

\frac{1}{5 x ^{\frac{4}{5}}}

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{5 x ^{\frac{4}{5}}}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[5]{(x^2+x/(x+1)}) ?
The derivative of \sqrt[5]{(x^2+x/(x+1)}) is 1/(5x^{4/5)}
What is the first derivative of \sqrt[5]{(x^2+x/(x+1)}) ?
The first derivative of \sqrt[5]{(x^2+x/(x+1)}) is 1/(5x^{4/5)}