CPM Homework Help : APCALC Problem 3-75

Differentiate the following expressions.

Hint:

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 $n$ .

$\frac { d } { d x } ( 6 ^ { 3 } )$
Hint (a):
$y = 6^3$ is a horizontal line.

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

$\frac { d } { d t } ( t ^ { - 9 } )$
Answer (c):
$−9t^{−10}$

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