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

The derivative of f(x)=\sqrt[5]{x^4} is (4x^3)/(5(x^4)^{4/5)}

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

The first derivative of f(x)=\sqrt[5]{x^4} is (4x^3)/(5(x^4)^{4/5)}

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derivative

\frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{5 ( x ^{4} ) ^{\frac{4}{5}}} \cdot 4 x^{3}

Simplify

\frac{1}{5 ( x ^{4} ) ^{\frac{4}{5}}} \cdot 4 x^{3} : \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}}

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}}

What is the derivative of f(x)=\sqrt[5]{x^4} ?
The derivative of f(x)=\sqrt[5]{x^4} is (4x^3)/(5(x^4)^{4/5)}
What is the first derivative of f(x)=\sqrt[5]{x^4} ?
The first derivative of f(x)=\sqrt[5]{x^4} is (4x^3)/(5(x^4)^{4/5)}