2.2 Basic Differentiation Rules and Rates of Change (Part 1) Colorado National Monument Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2003

Objectives Find the derivative of a function using the Constant Rule. Find the derivative of a function using the Power Rule. Find the derivative of a function using the Constant Multiple Rule. Find the derivative of a function using the Sum and Difference Rules. Find the derivative of the sine function and of the cosine function.

Rate of Change

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.

We saw that if , . This is part of a pattern. examples: power rule

Examples:

Example Find the slope of the graph of f(x)=x4 when (a) x= -1, (b) x=0 and (c) x=1.

Example Find an equation of the tangent line to the graph of f(x)=x2 when x= -2.

constant multiple rule: examples:

Examples: Find the derivative

Examples: Find the derivative

Examples: Find the derivative

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

Sine and Cosine rules:

Homework 2.2 (page 115) #3-63 odd