2.5 Basic Differentiation Properties 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.

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:

The Sum Rule: Example: The Difference Rule: Example:

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

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

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