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Popular >

derivative of \sqrt[6]{x-x^2}

Solution

\frac{d}{d x} (6 x - x^{2})

Solution

\frac{1 - 2 x}{6 ( x - x ^{2} ) ^{\frac{5}{6}}}

Solution steps

\frac{d}{d x} (6 x - x^{2})

Apply the chain rule:

\frac{1}{6 ( x - x ^{2} ) ^{\frac{5}{6}}} \frac{d}{d x} (x - x^{2})

= \frac{1}{6 ( x - x ^{2} ) ^{\frac{5}{6}}} \frac{d}{d x} (x - x^{2})

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

= \frac{1}{6 ( x - x ^{2} ) ^{\frac{5}{6}}} (1 - 2 x)

Simplify

\frac{1}{6 ( x - x ^{2} ) ^{\frac{5}{6}}} (1 - 2 x) : \frac{1 - 2 x}{6 ( x - x ^{2} ) ^{\frac{5}{6}}}

= \frac{1 - 2 x}{6 ( x - x ^{2} ) ^{\frac{5}{6}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[6]{x-x^2} ?
The derivative of \sqrt[6]{x-x^2} is (1-2x)/(6(x-x^2)^{5/6)}
What is the first derivative of \sqrt[6]{x-x^2} ?
The first derivative of \sqrt[6]{x-x^2} is (1-2x)/(6(x-x^2)^{5/6)}