Solve d/dt(2t^4/3-3t^2/3)=

$$\frac { d } { d t } ( 2 t ^ { 4 / 3 } - 3 t ^ { 2 / 3 } ) =$$

Evaluate

$$\frac{8\sqrt[3]{t}}{3}-\frac{2}{\sqrt[3]{t}}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{4}{3}\times 2t^{\frac{4}{3}-1}+\frac{2}{3}\left(-3\right)t^{\frac{2}{3}-1}$$

Multiply \frac{4}{3} times 2.

$$\frac{8}{3}t^{\frac{4}{3}-1}+\frac{2}{3}\left(-3\right)t^{\frac{2}{3}-1}$$

Subtract 1 from \frac{4}{3}.

$$\frac{8}{3}\sqrt[3]{t}+\frac{2}{3}\left(-3\right)t^{\frac{2}{3}-1}$$

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

$$\frac{8}{3}\sqrt[3]{t}-2t^{\frac{2}{3}-1}$$

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

$$\frac{8}{3}\sqrt[3]{t}-2t^{-\frac{1}{3}}$$

Differentiate w.r.t. t

$$\frac{8}{9t^{\frac{2}{3}}}+\frac{2}{3t^{\frac{4}{3}}}$$