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MAT 1234Calculus I
Section 2.3 Part II
Differentiation Formulas
http://myhome.spu.edu/lauw
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
