### Home > APCALC > Chapter 3 > Lesson 3.2.3 > Problem3-75

3-75.

Differentiate the following expressions.

## Power Rule

Since the beginning of this chapter, you have used the Power Rule to write slope functions of polynomial functions of the form $f(x) = x^n$where $n$is a positive integer. However, the Power Rule extends to all real values of $n$.

If $f(x) = x^n$, then $f^\prime(x) = nx^{n–1}$for all real values of $n$.

1. $\frac { d } { d x } ( 6 ^ { 3 } )$

$y = 6^3$ is a horizontal line.

1. $\frac { d } { d x } ( \frac { 2 } { 5 } x ^ { 15 } - \frac { 3 } { 4 } x ^ { 2 } )$

1. $\frac { d } { d t } ( t ^ { - 9 } )$

$−9t^{−10}$

1. $\frac { d } { d m } ( m ^ { 3 / 4 } )$