Solve (-t)^frac{2{3}}

$$( - t ) ^ { \frac { 2 } { 3 } }$$

Evaluate

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

Solution Steps

Expand \left(-t\right)^{\frac{2}{3}}.

$$\left(-1\right)^{\frac{2}{3}}t^{\frac{2}{3}}$$

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

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

For any term t, t\times 1=t and 1t=t.

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

Differentiate w.r.t. t

$$\frac{2}{3\sqrt[3]{t}}$$

Steps Using Definition of a Derivative

Expand \left(-t\right)^{\frac{2}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(-1\right)^{\frac{2}{3}}t^{\frac{2}{3}})$$

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

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

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

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

Subtract 1 from \frac{2}{3}.

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