chapter3: differentiation derivatives of trigonometric functions: chain rule: implicit diff....
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Chapter3: Differentiation
xxdx
dcos)(sin
xxdx
dsin)(cos
xxdx
d 2sec)(tan
xxxdx
dcotcsc)(csc
xxxdx
dtansec)(sec
xxdx
d 2csc)(cot
DERIVATIVES OF TRIGONOMETRIC FUNCTIONS:
)(')(')(' xgxgfxH Chain Rule:
Implicit diff.
))(('
1' )(
11
xffxf
axg
xgxg
dx
da ln
1
)(
)(')(log
)(
)(')(ln
xg
xgxg
dx
d
x
xx '
)(')()()(')()( xgxfxgxfxgxfdx
d
Derivative Product Rule
2)]([
)(')()()('
)(
)(
xg
xgxfxgxf
xg
xf
dx
d
Derivative Quotient Rule Derivative of exponential
)(ln)( aaadx
d xx
0a
ax
xf
at
diff )(
ax
xf
at
cont )(
exist
)(lim xfax
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) others
Exam-2 Problems
)2()(kf
Chapter3: Differentiation
The slope of the tangent line
)2(' fFind
The slope of the tangent line The rate of change
Exam-2 Problems
)9('y
)0('/1 f )8/(' s
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Sec 3.7: Implicit Differentiation
Sec 3.7: Implicit Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Sec 3.7: Implicit Differentiation
Sec 3.7: Implicit Differentiation
Sec 3.7: Implicit Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) others
Exam-2 Problems
)2()(kf
(Sketch and find the slopes)
Sec 3.9: Inverse Trigonometric Functions
Sec 3.9: Inverse Trigonometric Functions
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) others
Exam-2 Problems
)2()(kf
Chapter3: Differentiation
)(
)(lim
xg
xfax 0
0
)('
)('lim
)(
)(lim
xg
xf
xg
xfaxax
Chapter3: Differentiation
Sec 3.5: Derivatives Of Trigonometric Functions
Sec 3.5: Derivatives Of Trigonometric Functions
Sec 3.5: Derivatives Of Trigonometric Functions
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) others
Exam-2 Problems
)2()(kf
Sec 3.5: Derivatives Of Trigonometric Functions
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) others
Exam-2 Problems
)2()(kf
Chapter3: Differentiation
Chapter3: Differentiation
TERM-121 Exam-2
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
1) Direct: Find the g’(2)
2) Indirect: Find the slope….
3) Find slope in different ways
4) Find
5) Find: lim
6) Find f’(x)
7) Others 1) linearization, 2) differential,
3) Related 4) rate, rate ofchange,
5) cont+diff,
Exam-2 Problems
)2()(kf
TERM-121 Exam-2
Chapter3: Differentiation
TERM-121 Exam-2
Chapter3: Differentiation
Chapter3: Differentiation
TERM-121 Exam-2
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Chapter3: Differentiation
Sec 3.11: Linearization and Differentials
Sec 3.11: Linearization and Differentials
Sec 3.11: Linearization and Differentials
Exa
mp
le:
F09
1
Sec 3.11: Linearization and Differentials
Example: F091
Sec 3.11: Linearization and Differentials
Example: F091
Sec 3.11: Linearization and Differentials