Derivative and Integral Rules
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Transcript of Derivative and Integral Rules
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DERIVATIVE RULES
Power: ( ) 1nd n
x nxdx
= Trig: ( )sin cosd
x xdx
=
Exponential: ( ) lnxd
a adx
= xa ( )cos sind
x xdx
=
Product: ( )( ) ( ) ( ) ( ) ( ) ( )d
f x g x f x g x g x f xdx
= + ( ) 2tan secd
x xdx
=
Quotient:( )
2
( ) ( ) ( ) ( ) ( )
( ) ( )
d f x g x f x f x g x
dx g x g x
=
( ) 2cot csc
dx x
dx=
Chain: ( )( ( )) ( ( )) ( )d f g x f g x g xdx = ( )sec sec tand x x xdx =
Log: ( )1
lnd
xdx x
= ( )csc csc cotd
x x xdx
=
Inverse Trig:
( ) 21
arcsin1
dx
dx x=
Hyperbolic:
( )sinh cosh
dx x
dx=
( ) 21
arctan1
dx
dx x=
+ ( )cosh sinh
dx x
dx=
( )2
1arcsec
1
dx
dx x x=
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INTEGRAL RULES
Power: 11
, 11
n nx dx x c n
n
+= ++
Trig: sin cosxdx x c= +
Exponential:1
ln
xa dx a c
a=
x + cos sinxdx x c= +
Log:1
lndx x cx
= + 2sec tanxdx x c= +
2csc cotxdx x c= +
sec tan secx xdx x c= +
Inverse Trig:2
arcsin1
dx x cx
=
+
csc cot cscx xdx x c= +
2arctan
1
dxx c
x= +
+
2arcsec
1
dxx c
x x= +
Hyperbolic: sinh coshxdx x c= +
cosh sinhxdx x c= +
