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Popular >

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

Solution

derivative of

Solution

\frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{5}{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 x ^{4}}{6 ( x ^{5} ) ^{\frac{5}{6}}}

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

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=\sqrt[6]{x^5} ?
The derivative of f(x)=\sqrt[6]{x^5} is (5x^4)/(6(x^5)^{5/6)}
What is the first derivative of f(x)=\sqrt[6]{x^5} ?
The first derivative of f(x)=\sqrt[6]{x^5} is (5x^4)/(6(x^5)^{5/6)}