Solve (64s)^frac{1{3}}

$$( 64 s ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$4\sqrt[3]{s}$$

Solution Steps

Expand \left(64s\right)^{\frac{1}{3}}.

$$64^{\frac{1}{3}}s^{\frac{1}{3}}$$

Calculate 64 to the power of \frac{1}{3} and get 4.

$$4s^{\frac{1}{3}}$$

Differentiate w.r.t. s

$$\frac{4}{3s^{\frac{2}{3}}}$$

Steps Using Definition of a Derivative

Expand \left(64s\right)^{\frac{1}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(64^{\frac{1}{3}}s^{\frac{1}{3}})$$

Calculate 64 to the power of \frac{1}{3} and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}s}(4s^{\frac{1}{3}})$$

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

$$\frac{1}{3}\times 4s^{\frac{1}{3}-1}$$

Multiply \frac{1}{3} times 4.

$$\frac{4}{3}s^{\frac{1}{3}-1}$$

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

$$\frac{4}{3}s^{-\frac{2}{3}}$$