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Calculus!/Trig
Basic Differentiation and Integration Rules and Trig Identities
51
Mathematics
12th Grade
12/03/2008
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Term
d/dx (k)
 Definition
0
Term
d/dx (un)
 Definition
nuu-1 (du/dx)
Term
d/dx (uv)
 Definition
u(dv/dx) + v(du/dx)
Term
d/dx (u/v)
 Definition

(v(du/dx) - u(dv/dx))/v2

 

(ho dhi - hi dho)/ho ho

Term
d/dx (ku)
 Definition
k (du/dx)
Term
d/dx (u±v)
 Definition
(du/dx) ± (dv/dx)
Term
d/dx (sin u)
 Definition
cos u (du/dx)
Term
d/dx (cos u)
 Definition
-sin u (du/dx)
Term
d/dx (tan u)
 Definition
sec2 u (du/dx)
Term
d/dx (cot u)
 Definition
-csc2 u (du/dx)
Term
d/dx (sec u)
 Definition
sec u tan u (du/dx)
Term
d/dx (csc u)
 Definition
-csc u cot u (du/dx)
Term
d/dx (eu)
 Definition
eu (du/dx)
Term
d/dx (au)
 Definition
(ln a)au (du/dx)
Term
d/dx (ln u)
 Definition
(1/u) (du/dx)
Term
d/dx (logau)
 Definition
(1/[(ln a) u]) (du/dx)
Term
d/dx (sin-1 u)
 Definition
[1/√(1-u2)] (du/dx)
Term
d/dx (cos-1 u)
 Definition
[-1/√(1-u2)] (du/dx)
Term
d/dx (tan-1 u)
 Definition
[1/(1+u2)] (du/dx)
Term
d/dx (cot-1 u)
 Definition
[-1/(1+u2)] (du/dx)
Term
d/dx (sec-1 u)
 Definition
[1/(|u| √(u2- 1))] (du/dx)
Term
d/dx (csc-1 u)
 Definition
[-1/(|u| √(u2- 1))] (du/dx)
Term
∫k f(u) du
 Definition
k ∫ f(u) du
Term
∫ [f(u) + g(u)] du
 Definition
∫ f(u) du + ∫ g(u) du
Term
∫ du
 Definition
u + C
Term
∫ un du
 Definition
(un+1)/(n+1) + C, n≠1
Term
∫ (1/u) du
 Definition
ln |u| + C
Term
∫eu du
 Definition
eu + C
Term
∫au du
 Definition
(1/ln a) au + C
Term
∫ sin(u) du
 Definition
-cos(u) + C
Term
∫ cos(u) du
 Definition
sin(u) + C
Term
∫ tan(u) du
 Definition
-ln|cos(u)| + C
Term
∫ cot(u) du
 Definition
ln|sin(u)| + C
Term
∫ sec(u) du
 Definition
ln|sec(u) + tan(u)| + C
Term
∫ csc(u) du
 Definition
-ln|csc(u) + cot(u)| + C
Term
∫ sec2(u) du
 Definition
tan(u) + C
Term
∫ csc2(u) du
 Definition
-cot(u) + C
Term
∫ sec(u)tan(u) du
 Definition
sec(u) + C
Term
∫ csc(u)cot(u) du
 Definition
-csc(u) + C
Term
∫ [1/√(1-u2)] du
 Definition
sin-1 u + C
Term

∫ [1/(1+u2)] du

Definition
tan-1 u + C
Term
∫[1/(|u|√(u2-1))] du
 Definition
sec-1 u +C
Term
Trig: Pythagorean Identities
 Definition

sin2 u + cos2 u = 1

1+ tan2 u = sec2 u

1 + cot2 u = csc2 u

Term
sin (u+v)
 Definition
sin u cos v + cos u sin v
Term
sin (u-v)
 Definition
sin u cos v - cos u sin v
Term
cos (u+v)
 Definition
cos u cos v - sin u sin v
Term
cos (u-v)
 Definition
cos u cos v + sin u sin v
Term
tan (u+v)
 Definition
(tan u + tan v)/(1- tan u tan v)
Term
tan (u-v)
 Definition
(tan u - tan v)/(1+ tan u tan v)
Term
sin (2u)
 Definition
2 sin u cos u
Term
cos (2u)
 Definition

cos2 u - sin2 u

2 cos2 u - 1

1 - 2 sin2u

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