Page 21 - Calc for the Clueless

We must multiply out the top, but we do not multiply the bottom.

Example 5—

Find g'(x) using the definition of derivative if

Rationalize the numerator.

We can't keep using the definition of derivative. If we had a complicated function, it would take forever. We
will list the rules, interpret them, and give examples. Proofs are found in most calculus books.

Rule 1

If f(x) = c, f'(x) = O. The derivative of a constant is 0.

Rule 2

If f(x) = x, f'(x) = 1.