Chapter 3.3, Problem 1E

To determine

The derivative of the function $g\left(t\right)=6t^{\frac{5}{3}}$ .

Answer to Problem 1E

The derivative of the function $g\left(t\right)=6t^{\frac{5}{3}}$ is $10t^{\frac{2}{3}}$ .

Explanation of Solution

Given:

The function is $g\left(t\right)=6t^{\frac{5}{3}}$ .

Calculation:

Differentiate both sides of the equation using power rule as follows:

  $\begin{array}{c}{g}^{\prime }\left(t\right)=\frac{d}{dt}\left(6t^{\frac{5}{3}}\right)\\ =6\left(\frac{5}{3}{t}^{\frac{5}{3}-1}\right)\\ =10t^{\frac{2}{3}}\end{array}$

Thus, the derivative of the function $g\left(t\right)=6t^{\frac{5}{3}}$ is $10t^{\frac{2}{3}}$ .