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Known and Loved Derivatives - Lecture Notes | MATH 162, Study notes of Calculus

State University of New York at Canton (SUNY)Calculus
Prof. Daniel Gagliardi

Known and Loved Derivatives Material Type: Notes; Professor: Gagliardi; Class: CALCULUS II; Subject: Mathematics; University: SUNY College of Technology at Canton; Term: Spring 2013;

Typology: Study notes

2012/2013

Uploaded on 04/15/2013

rcollins0618
rcollins0618 🇺🇸

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Known and Loved Derivatives
1.
   
)()()(
1
xfxfnxf
dx
d
nn



2.
)())(cos())(sin( xfxfxf
dx
d

3.
)())(sin())(cos( xfxfxf
dx
d

4.
)())((sec))(tan(
2
xfxfxf
dx
d

5.
)())(tan())(sec())(sec( xfxfxfxf
dx
d

6.
)())(cot())(csc())(csc( xfxfxfxf
dx
d

7.
)())((csc))(cot(
2
xfxfxf
dx
d

8.
)(
)(
))(ln( xf
xf
xf
dx
d

9.
10.
)ln()(
)()(
axfaa
dx
d
xfxf


11.
)(
)(1
1
))((sin
2
1
xf
xf
xf
dx
d




12.
)(
)(1
1
))((tan
2
1
xf
xf
xf
dx
d




13.
)(
1)()(
1
))((sec
2
1
xf
xfxf
xf
dx
d




Some Differentiation Theorems
1.
 
)()()()( xgxfxgxf
dx
d



2.
 
)()( xfcxcf
dx
d

3.
 
)()()()()()( xfxgxgxfxgxf
dx
d



4..
)(
)()()()(
)(
)(
2
xg
xgxfxfxg
xg
xf
dx
d












Partial preview of the text

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Known and Loved Derivatives

1

f x n f x f x

dx

d n n



sin( f ( x )) cos( f ( x )) f ( x )

dx

d

cos( f ( x )) sin( f ( x )) f ( x )

dx

d

tan( ( )) sec ( ( )) ( )

2

f x f x f x

dx

d

sec( f ( x )) sec( f ( x ))tan( f ( x )) f ( x )

dx

d

csc( f ( x )) csc( f ( x ))cot( f ( x )) f ( x )

dx

d

cot( ( )) csc ( ( )) ( )

2

f x f x f x

dx

d

ln( ( ))

f x

f x

f x

dx

d

( ) ()

e e f x

dx

d

f x fx

( )ln( )

( ) ()

a a f x a

dx

d

f x fx

( )

1 ( )

1

sin ( ( ))

2

1

f x

f x

f x

dx

d

 







tan ( ( ))

2

1

f x

f x

f x

dx

d



( )

( ) ( ) 1

1

sec ( ( ))

2

1

f x

f x f x

f x

dx

d

 







Some Differentiation Theorems

 f ( x ) g ( x ) f ( x ) g ( x )

dx

d

 cf ( x ) cf ( x )

dx

d

 f ( x ) g ( x ) f ( x ) g ( x ) g ( x ) f ( x )

dx

d

2

g x

g x f x f x g x

g x

f x

dx

d