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

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

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

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

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derivative of

\frac{1}{5 r ^{\frac{4}{5}}}

Solution steps

Apply radical rule:

= \frac{d}{d r} (r^{\frac{1}{5}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{5} r^{\frac{1}{5} - 1}

Simplify

\frac{1}{5} r^{\frac{1}{5} - 1} : \frac{1}{5 r ^{\frac{4}{5}}}

= \frac{1}{5 r ^{\frac{4}{5}}}

\int (\frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{2} ( x )}) d x

(\frac{1}{y ^{2}} - \frac{2}{y ^{4}}) (y + 8 y^{3})

\int_{- 2}^{3} \frac{35}{x ^{4}} d x

\frac{d y}{d x} = e^{2 x} + 7 y

\frac{d}{d x} (\frac{y}{x - y})

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