If the derivative of a function is its slope, then for a constant function, the derivative must be zero.

1. 2.3 Basic Differentiation Formulas The derivative of a constant is zero. If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example:

2. Power Rule: If n is any real number, then Examples: Constant Multiple Rule: If c is a constant and f is differentiable function, then Examples:

3. The Sum Rule: Example: The Difference Rule: Example:

4. Horizontal tangents occur when slope = zero. Example: Find the horizontal tangents of: Plugging the x values into the original equation, we get:

6. slope Consider the function We could make a graph of the slope: Now we connect the dots! The resulting curve is a cosine curve.

7. slope We can do the same thing for The resulting curve is a sine curve that has been reflected about the x-axis.

8. 2.4 The Product and Quotient Rules

9. The Product Rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

10. The Quotient Rule: or Example:

11. We can find the derivative of thetangent function by using the quotient rule.

12. Derivatives of the remaining trigonometric functions can be determined the same way.