What is the derivative of \sqrt[6]{x^5} ?

The derivative of \sqrt[6]{x^5} is 5/(6x^{1/6)}

What is the first derivative of \sqrt[6]{x^5} ?

The first derivative of \sqrt[6]{x^5} is 5/(6x^{1/6)}

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\frac{5}{6 x ^{\frac{1}{6}}}

Solution steps

Apply the chain rule:

\frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \frac{d}{d x} (x^{5})

= \frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \cdot 5 x^{4}

Simplify

\frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \cdot 5 x^{4} : \frac{5}{6 x ^{\frac{1}{6}}}

= \frac{5}{6 x ^{\frac{1}{6}}}

What is the derivative of \sqrt[6]{x^5} ?
The derivative of \sqrt[6]{x^5} is 5/(6x^{1/6)}
What is the first derivative of \sqrt[6]{x^5} ?
The first derivative of \sqrt[6]{x^5} is 5/(6x^{1/6)}