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Popular >

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

Solution

derivative of

7 x^{6} - x^{e}

Solution

\frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}} - e x^{e - 1}

Solution steps

\frac{d}{d x} (7 x^{6} - x^{e})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[7]{x^6}-x^e ?
The derivative of \sqrt[7]{x^6}-x^e is (6x^5)/(7(x^6)^{6/7)}-ex^{e-1}
What is the first derivative of \sqrt[7]{x^6}-x^e ?
The first derivative of \sqrt[7]{x^6}-x^e is (6x^5)/(7(x^6)^{6/7)}-ex^{e-1}