What is the derivative of \sqrt[7]{x^2} ?

The derivative of \sqrt[7]{x^2} is 2/(7x^{5/7)}

What is the first derivative of \sqrt[7]{x^2} ?

The first derivative of \sqrt[7]{x^2} is 2/(7x^{5/7)}

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\frac{2}{7 x ^{\frac{5}{7}}}

Solution steps

Apply the chain rule:

\frac{1}{7 ( x ^{2} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{2})

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

\frac{1}{7 ( x ^{2} ) ^{\frac{6}{7}}} \cdot 2 x : \frac{2}{7 x ^{\frac{5}{7}}}

= \frac{2}{7 x ^{\frac{5}{7}}}

What is the derivative of \sqrt[7]{x^2} ?
The derivative of \sqrt[7]{x^2} is 2/(7x^{5/7)}
What is the first derivative of \sqrt[7]{x^2} ?
The first derivative of \sqrt[7]{x^2} is 2/(7x^{5/7)}