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Popular >

derivative of \sqrt[7]{x^6}

Solution

derivative of

Solution

\frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

Solution steps

Apply the chain rule:

\frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{6})

= \frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{6})

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

= \frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \cdot 6 x^{5}

Simplify

\frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \cdot 6 x^{5} : \frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

= \frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

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(\partial ^2)/(\partial x\partial y)(x^5+x^2y+x+3)

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[7]{x^6} ?
The derivative of \sqrt[7]{x^6} is (6x^5)/(7(x^6)^{6/7)}
What is the first derivative of \sqrt[7]{x^6} ?
The first derivative of \sqrt[7]{x^6} is (6x^5)/(7(x^6)^{6/7)}