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)}

derivative of

5 r

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

Solution steps

\frac{d}{d r} (5 r)

Apply radical rule:

n a = a^{\frac{1}{n}}

= \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

d er i v a t i v e (\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

t an g e n t y = 2 x^{3} - x^{2} + 9, (2, 21)

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)}