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# Power Rule for AP Calculus

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By McGraw-Hill Professional
Updated on Oct 24, 2011

Practice problems for these concepts can be found at: Differentiation Practice Problems for AP Calculus

If f (x) = c where c is a constant, then f '(x) = 0.

If f (x) = xn where n is a real number, then f '(x) = nxn-1.

If f (x) = cxn where c is a constant and n is a real number, then f '(x) = cnxn-1.

### Summary of Derivatives of Algebraic Functions

#### Example 1

If f (x) = 2x3, find (a) f '(x), (b) f '(1) and (c) f '(0)

Note that (a) f'(x) = 6x2, (b) f'(1) = 6(1)2 = 6, and (c) f'(0) = 0.

#### Example 3

Here are several examples of algebraic functions and their derivatives:

#### Example 4

Using a calculator, find f '(x) and f '(3) if

There are several ways of finding f '(x) and f'(9)using a calculator. One way to use the d [differentiate] function. Go to the Home screen. Select F3-Calc and then select d [differentiate]. Enter The result is To find f '(3), enter

Practice problems for these concepts can be found at: Differentiation Practice Problems for AP Calculus

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