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

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

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

7. We can do the same thing for
slope
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 the tangent function by using the quotient rule.

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