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Calculus AB Rules
Differentiation and Integration Rules
13
Mathematics
12th Grade
04/05/2009
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Term
d/dx(au)
 Definition
au·ln(a)·du/dx
Term
d/dx(ln|u|)
 Definition
1/u ·du/dx
Term
d/dx(loga |u|)
 Definition

Change the base

d/dx(ln|u|/ln(a))

 

1/lna ·1/u ·du/dx
Term
∫au du
 Definition
1/ln(a) ·au + C
Term
∫1/u du
 Definition
ln|u| + C
Term
∫eu du
 Definition
eu + C
Term
d/dx(sin-1u)
 Definition

1 du/dx

√(1 - u2) 
Term
d/dx (cos-1 u)
 Definition

-1 du

√(1 - u2) dx
Term
d/dx(tan-1 u)
 Definition

1 du

(1 + u2) dx
Term
∫1/√(a2 - u2)du
 Definition
sin-1(u/a) + C
Term
d/dx(sec-1 u)
 Definition

1  du/dx

u√(u2 - 1)
Term
∫1/(a2 + u2) du
 Definition
(1/a) tan-1 (u/a) + C
Term
∫1/(u√(u2 - a2) du
 Definition
(1/a) sec-1 (u/a) + C
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