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

The derivative of f(x)=\sqrt[7]{x^6} is (6x^5)/(7(x^6)^{6/7)}

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

The first derivative of f(x)=\sqrt[7]{x^6} is (6x^5)/(7(x^6)^{6/7)}

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derivative of

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