1. Derivative Rules
3.3

2. Derivative of a Constant
For any constant C,
Suppose f(x) is a constant function, that is, f(x) = C, where C is a constant. Since the value of the function never changes, the instantaneous rate of change must be zero.
Examples:

3. Derivatives of Powers Derivative of a Power Examples:
If n is any real number (n may or may not be an integer),
Another way to remember this rule is “power in front, reduce the power by one”.
Examples:

4. constant multiple rule:
examples:

5. constant multiple rule:
sum and difference rules:
(Each term is treated separately)

6. Derivatives of trig functions

7. Example: Find the derivative of:

8. Example: Find the derivative of:

9. Example: Find the derivative of:

10. Example: Find the derivative of:

11. Example:
Find the horizontal tangents of:
Horizontal tangents occur when slope = zero.
Plugging the x values into the original equation, we get:
(The function is even, so we only get two horizontal tangents.)

12. Higher Order Derivatives
2nd derivative
3rd derivative
1st derivative

13. Find the first 4 derivatives of:

14. Find the derivative of:
We have to foil first!

15. Find the slope of the curve y = 2cos(x) at: