After the test… No calculator 3. Given the function defined by for a) State whether the function is even or odd. Justify. b) Find f’(x) c) Write an equation of the line tangent to the graph of f at the point where x = 0.

After the test 3. Given the function defined by for a) State whether the function is even or odd. Justify.

After the test 3. Given the function defined by for b) Find f’(x)

After the test 3. Given the function defined by for c) Write an equation of the line tangent to the graph of f at the point where x = 0.

2-4: The Chain Rule ©2002 Roy L. Gover ( Objectives: Apply the chain rule Practice simplifying derivatives Use the chain rule with trig functions

Important Idea The chain rule is used to find the derivative of a composite function. It is the derivative of the outside function composed of the inside function times the derivative of the inside function.

Definition The chain rule: Let y and u be differentiable functions then:

Definition-I like this better The chain rule: Let f and g be differentiable functions then:

Example Find : outside function inside function Let and

Example Find : Let and

Example Find :

Example Differentiate:

Example Differentiate:

Try This Find a function for the slope of the tangent line:

Example Find all points on the graph of: for which f ’ (x)= 0 or f ’ (x) does not exist.

Example Find all points on the graph of: for which f ’ (x)= 0 or f ’ (x) does not exist.

Solution

Analysis Where is the slope of f(x) positive and where is it negative? Where is the slope of f(x) =0?

Example Differentiate: Hint: re-write then use the power and chain rules

Try This Differentiate:

Example Find the derivative and simplify. Use the product rule first then find the derivative using the quotient rule: Review examples 7,8, & 9 on page 134

Example Find the derivative and simplify. Use the product rule first then find the derivative using the quotient rule: Review examples 7,8, & 9 on page 134

Assignment /1-19 odd

Try This Find the derivative and simplify: Hint: use the product, power & chain rules.

Try This Find the derivative and simplify: Hint: use the product, power & chain rules.

Warm-UP

HW?

Example Find :

Try This Find :

Example Find the derivative:

Example Find the derivative: Sometimes you will use the chain rule twice

Important Idea Memorize the differentiation rules summarized on page 136

Lesson Close Without using your notes or text, explain the chain rule.

Assignment Page 137/21-29 odd, odd,53,61,69