MAT 1234Calculus I

Section 2.3 Part II

Differentiation Formulas

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Math Major –INT?

Part II

WebAssign 2.3 Part II

Exam 1

Exam 1 is coming up. Resolve any problems before the exam.

Proficiency: Must able to do your HW problems on your own.

Able to state theorems. Review quiz solutions/comments. Turn in your tutoring bonus record on

Thursday.

Friendly Competition

Bring your HW notebook on Thursday. 5 notebooks will be selected for bonus

points.

Recall: Sum and Difference Rule

If , then)()( xvxuy )()( xvxuy

However,…

If , then

If , then

)()( xgxfy ( ) ( )y f x g x

)(

)(

xg

xfy

)(

)(

xg

xfy

?Why

Example

( ) ( ) where ( ) 1, ( )y f x g x f x g x x

1

1

y x

x

y

1

0 1

0

f x g x x

( ) ( )y f x g x

Product Rule

If ,

then

)()( xgxfy

)()()()( xgxfxgxfy

Example 6:

2

2 2

( ) (4 1)(3 1)

( ) (4 1) (3 1) (4 1)(3 1)

f x x x

f x x x x x

( ) ( )

( ) ( ) ( ) ( )

y f x g x

y f x g x f x g x

Quotient Rule

If

then

)(

)(

xg

xfy

2

( ) ( ) ( ) ( )

( )

f x g x f x g xy

g x

Example 7

2

2 1

xy

x

y

2)(

)()()()(

xg

xgxfxgxfy

Expectations

Must show the “formula” step when using the product/quotient rules

2 2

2 2

2

( ) (4 1) (3 1) (4 1)(3 1)

2 1 2 1

2 1

f x x x x x

x x x xy

x

Expectations

Must show “enough” details. Most points in the quizzes/exams are

given to the solution process/steps.

Classwork

Expectation for the Quiz Today

 

0

2 2

0

( ) ( )( ) lim

( )lim

h

h

f x h f xf x

h

x h x

h