What is the derivative of \sqrt[5]{2x} ?

The derivative of \sqrt[5]{2x} is (2^{1/5})/(5x^{4/5)}

What is the first derivative of \sqrt[5]{2x} ?

The first derivative of \sqrt[5]{2x} is (2^{1/5})/(5x^{4/5)}

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derivative of

\frac{2 ^{\frac{1}{5}}}{5 x ^{\frac{4}{5}}}

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 ^{\frac{1}{5}}}{5 x ^{\frac{4}{5}}}

x \to 3 lim (4 x^{2} - 3 x + 2)

\int \frac{1}{z ^{2} + 6 z + 10} d z

\frac{d}{d x} (3 x^{2} + 7 x - 2)

\frac{d x}{d y} = x 1 - y^{2}

What is the derivative of \sqrt[5]{2x} ?
The derivative of \sqrt[5]{2x} is (2^{1/5})/(5x^{4/5)}
What is the first derivative of \sqrt[5]{2x} ?
The first derivative of \sqrt[5]{2x} is (2^{1/5})/(5x^{4/5)}