CALCULUS - CLUTCH CH.6: DERIVATIVES (PART...
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CALCULUS - CLUTCH
CH.6: DERIVATIVES (PART 1)
INTRO TO DERIVATIVES
● A derivative is a _________________ .
● Notations for derivatives are: _______ , _______ and _______
● To find the derivative (__________), we use the following:
COMPUTING DERIVATES:
EXAMPLE 1: Find the derivative of ,
EXAMPLE 2: Given
A) Find the derivative ,
B) Find the slope of the line tangent at
EXAMPLE 3: Find the derivative of
Step Box:
1. Find f(x+h) 2. Input into formula 3.Simplify + Combine LT 4.Apply limit
CALCULUS - CLUTCH
CH.6: DERIVATIVES (PART 1)
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PRATICE: INTRO TO DERIVATIVES
PROBLEM: Find the derivative using the following equation:
( ) ( )
1. Find the derivative of ( )
A
B
C
( )
D
( )
Step Box:
1. Find f(x+h) 2. Input into formula 3.Simplify + Combine LT 4.Apply limit
CALCULUS - CLUTCH
CH.6: DERIVATIVES (PART 1)
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PROBLEM: Find the derivative using the following equation:
( ) ( )
2. Find the derivative of ( ) √
A √
B
C
√
D √
Step Box:
1. Find f(x+h) 2. Input into formula 3.Simplify + Combine LT 4.Apply limit
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CH.6: DERIVATIVES (PART 1)
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DERIVATIVE RULES
● To avoid using _______________ , we have derivative rules.
RULE FORMULA EXAMPLE
Constant Rule
Coefficient Rule
Power Rule
POPERTY FORMULA EXAMPLE
Constant Property
Addition Property
Difference Property
EXAMPLE 1: Derive the following:
A)
C)
B)
D)
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CH.6: DERIVATIVES (PART 1)
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PRACTICE:DERIVATIVE RULES
PROBLEM: Derive the following:
1.
2.
A
B
C
D
A
B
C
D
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CH.6: DERIVATIVES (PART 1)
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PROBLEM: Derive the following:
3.
4.
A
B
C
D
A
B
C
D
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CH.6: DERIVATIVES (PART 1)
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PRODUCT RULE
● Product rule is used when two functions (multiply / divide).
EXAMPLE 1
Given , find
EXAMPLE 2
Given , find
EXAMPLE 3
Given , find
Product Rule
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CH.6: DERIVATIVES (PART 1)
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PRACTICE: PRODUCT RULE
PROBLEM: Derive the following:
1. ( ) ( )( )
A ( )( ) ( )( ) B ( )( ) ( )( )
C ( )( ) ( )( ) D ( )( ) ( )( )
2. ( ) ( )(√ )
A ( )(√ ) (
√ ) ( ) B ( )(√ ) (
√ ) ( )
C ( )( ) (
√ ) (√ ) D ( )(√ ) (
√ ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
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CH.6: DERIVATIVES (PART 1)
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PROBLEM: Derive the following:
3. ( ) ( )(
)
A ( )( ) ( )( ) B ( ) (
) (
) ( )
C ( )( ) (
) (
) D ( ) (
) (
) ( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
CALCULUS - CLUTCH
CH.6: DERIVATIVES (PART 1)
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QUOTIENT RULE
●Quotient rule is used when two functions (multiply / divide).
EXAMPLE 1
Given
, find
EXAMPLE 2
Given
, find
EXAMPLE 3
Given
, find
Product Rule
Quotient Rule
CALCULUS - CLUTCH
CH.6: DERIVATIVES (PART 1)
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PRACTICE: QUOTIENT RULE
PROBLEM: Derive the following:
1.
2.
A
B
C
D
A
B
C
D
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CH.6: DERIVATIVES (PART 1)
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CHAIN RULE
● Chain rule is used to derive ____________________ functions.
● Composite functions are written in the form of:
EXAMPLE 1: Derive the following,
A)
B)
C)
D)
E)
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CH.6: DERIVATIVES (PART 1)
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PRACTICE: CHAIN RULE
1. ( ) ( )
A ( ) B ( )
C ( ) D ( )
2. ( ) [( ) ( )]
A [( ) ( )] B [( ) ( )] [ ( ) ( ) ( ) ]
C [ ( ) ( )] D [( ) ( )] [ ( ) ( ) ( ) ]
( ) ( ( )) ( ) ( ( )) ( )
( ) ( ( )) ( ) ( ( )) ( )
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PROBLEM: Derive the following:
3. ( ) (
)
A ( )( ) ( )( ) B ( )( ) ( )( )
C ( )( ) ( )( ) D ( )( ) ( )( )
4. ( ) √
√
A ( )
( )
B ( )
( )
C ( )
( )
D ( )
( )
A
√
B
√
C
√
D
√
( ) ( ( )) ( ) ( ( )) ( )
( ) ( ( )) ( ) ( ( )) ( )
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