What is the derivative of \sqrt[7]{x^4} ?

The derivative of \sqrt[7]{x^4} is 4/(7x^{3/7)}

What is the first derivative of \sqrt[7]{x^4} ?

The first derivative of \sqrt[7]{x^4} is 4/(7x^{3/7)}

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\frac{4}{7 x ^{\frac{3}{7}}}

Solution steps

Apply the chain rule:

\frac{1}{7 ( x ^{4} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{4})

= \frac{1}{7 ( x ^{4} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{7 ( x ^{4} ) ^{\frac{6}{7}}} \cdot 4 x^{3}

Simplify

\frac{1}{7 ( x ^{4} ) ^{\frac{6}{7}}} \cdot 4 x^{3} : \frac{4}{7 x ^{\frac{3}{7}}}

= \frac{4}{7 x ^{\frac{3}{7}}}

What is the derivative of \sqrt[7]{x^4} ?
The derivative of \sqrt[7]{x^4} is 4/(7x^{3/7)}
What is the first derivative of \sqrt[7]{x^4} ?
The first derivative of \sqrt[7]{x^4} is 4/(7x^{3/7)}