3.3 Product Rule Tues Oct 27 Do Now Evaluate each 1) 2)

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Presentation transcript:

3.3 Product Rule Tues Oct 27 Do Now Evaluate each 1) 2)

HW Review p odds 5)3x^2 -221) 7)6x23) 9) 0 11) 13) 15) -5x^(-3/2) -2 17) 19)

HW Review p evens 6) 8) 10) -4 12) 14) 16) 18) 20) 22)

Not the Product Rule Consider our derivative rules so far. We do not know the derivative if 2 terms are multiplied together Note: the derivative of a product is NOT the product of the derivatives:

Proof

Product Rule Thm- Suppose that f(x) and g(x) are differentiable at x. Then: Ex: y = x e^x

Ex 1 Use the product rule to find

Ex 2 Find f’(x) if

Ex 3 Find the derivative of the function

Closure Hand in: Compute the derivative of Using the product rule HW: p.147 #1-3, 5, 13, 14, 17

3.3 Quotient Rule Wed Oct 28 Do Now Use the product rule to find the derivative: 1) 2)

HW Review: p.147 # ) 2) 3) 5) 871/64 13) 14) 6x )

Quotient Rule Thm- Suppose that f and g are differentiable at x and g(x) not equal to 0, then: This is especially useful when we cannot simplify the fraction.

Ex 1 Find the derivative of

Ex 2 Find the derivative of

Ex 3 Find the tangent line to the graph of f(x) at x = 1

Cases where the Product and Quotient rules are not needed Sometimes, it’s easier to simplify and use the power rule instead of the product or quotient rule Ex:

Applications Remember that the derivative may be used to represent rates such as speed. Now that we can differentiate more complicated functions, we can now apply these to other types of rates. Ex 7

Closure Journal Entry: Write about the product and quotient rules. What are the formulas? How do we use them? Do we need to use them for every problem? HW: p.147 #7-11, 15, 23, 25

Practice Thurs Oct 29 Do Now Find the derivative of each 1) 2)

HW Review p.147 # )23) -80 8)25) -3/4 9) 8/9 10) 27/32 11) 15) 1

Derivative Review Power Rule Product Rule Quotient Rule

3.3 Practice Start in class #1-18. Complete for HW

Closure Find the derivative of: HW: Finish worksheet p.203 #1-18

HW Review: wkst p.203 #1-18 1) 4x + 1 2) 3) 4) 5) 6) 7) 8) 9) 10)

HW Review # ) -5/4 12) -1/6 13) 7/16 14) -7/4 15) ) 1/2 17) 0 18) 1