Solve (8r)^1/3

$$( 8 r ) ^ { 1 / 3 }$$

Evaluate

$$2\sqrt[3]{r}$$

Solution Steps

Expand \left(8r\right)^{\frac{1}{3}}.

$$8^{\frac{1}{3}}r^{\frac{1}{3}}$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$2r^{\frac{1}{3}}$$

Differentiate w.r.t. r

$$\frac{2}{3r^{\frac{2}{3}}}$$

Steps Using Definition of a Derivative

Expand \left(8r\right)^{\frac{1}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(8^{\frac{1}{3}}r^{\frac{1}{3}})$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}r}(2r^{\frac{1}{3}})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{3}\times 2r^{\frac{1}{3}-1}$$

Multiply \frac{1}{3} times 2.

$$\frac{2}{3}r^{\frac{1}{3}-1}$$

Subtract 1 from \frac{1}{3}.

$$\frac{2}{3}r^{-\frac{2}{3}}$$