What is the derivative of f(x)=\sqrt[5]{x^2} ?

The derivative of f(x)=\sqrt[5]{x^2} is (2x)/(5(x^2)^{4/5)}

What is the first derivative of f(x)=\sqrt[5]{x^2} ?

The first derivative of f(x)=\sqrt[5]{x^2} is (2x)/(5(x^2)^{4/5)}

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derivative of

f (x) = 5 x^{2}

\frac{2 x}{5 ( x ^{2} ) ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} (5 x^{2})

Apply the chain rule:

\frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2})

= \frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2})

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

= \frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \cdot 2 x

Simplify

\frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \cdot 2 x : \frac{2 x}{5 ( x ^{2} ) ^{\frac{4}{5}}}

= \frac{2 x}{5 ( x ^{2} ) ^{\frac{4}{5}}}

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What is the derivative of f(x)=\sqrt[5]{x^2} ?
The derivative of f(x)=\sqrt[5]{x^2} is (2x)/(5(x^2)^{4/5)}
What is the first derivative of f(x)=\sqrt[5]{x^2} ?
The first derivative of f(x)=\sqrt[5]{x^2} is (2x)/(5(x^2)^{4/5)}