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Popular Calculus >

derivative of y=\sqrt[7]{x^3}-x^e

Solution

derivative of

y = 7 x^{3} - x^{e}

Solution

\frac{3 x ^{2}}{7 ( x ^{3} ) ^{\frac{6}{7}}} - e x^{e - 1}

Solution steps

\frac{d}{d x} (7 x^{3} - x^{e})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (7 x^{3}) - \frac{d}{d x} (x^{e})

\frac{d}{d x} (7 x^{3}) = \frac{3 x ^{2}}{7 ( x ^{3} ) ^{\frac{6}{7}}}

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

= \frac{3 x ^{2}}{7 ( x ^{3} ) ^{\frac{6}{7}}} - e x^{e - 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=\sqrt[7]{x^3}-x^e ?
The derivative of y=\sqrt[7]{x^3}-x^e is (3x^2)/(7(x^3)^{6/7)}-ex^{e-1}
What is the first derivative of y=\sqrt[7]{x^3}-x^e ?
The first derivative of y=\sqrt[7]{x^3}-x^e is (3x^2)/(7(x^3)^{6/7)}-ex^{e-1}