11 - Demonstarting Power Rule in Examples

Here are some examples to show how the power rule for differentiation is used to find the derivative of some power functions.

Example 1. Let y= x 4  , then dy dx =4 x 41 =4 x 3 .

Example 2. Let y= x 3.6  , then dy dx =3.6 x 3.61 =3.6 x 2.6 .

Example 3. Let y= x 5  , then dy dx =5 x 51 =5 x 6 .

Example 4. Let y= x 2  , then dy dx = 2 x 2 1

Example 5. Let y= x 2 3  , then dy dx = 2 3 x 2 3 1 = 2 3 x 1 3

Example 6. Let y= x π  , then dy dx =π x π1

Example 7. Let y= 1 x 5 = x 5  , then dy dx =5 x 51 =5 x 6 = 5 x 6