Section 2.3 Summary

Chapter 2
Models of Growth: Rates of Change

Section Summary

In this section we derived the Power Rule and the Constant Multiple Rule for differentiation:

Power Rule If \(n\) is any positive integer, then

\frac{d}{d t} t^{n} = n t^{n - 1}

Constant Multiple Rule If

f (t)

is any function that has a derivative, and c is any constant, then

\frac{d}{d t} c f (t) = c \frac{d f}{d t}

We also stated the Sum Rule:

Sum Rule If

f (t)

and

g (t)

are any functions that have derivatives, then

\frac{d}{d t} [f (t) + g (t)] = \frac{d f}{d t} + \frac{d g}{d t}

With these three rules in hand, we can easily find the symbolic derivative of any polynomial.