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Popular >

derivative of f(x)=\sqrt[3]{x^7}

Solution

derivative of

f (x) = 3 x^{7}

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

= \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

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

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

Simplify

\frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \cdot 7 x^{6} : \frac{7 x ^{6}}{3 ( x ^{7} ) ^{\frac{2}{3}}}

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

Graph

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Frequently Asked Questions (FAQ)

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