Cheatography
https://cheatography.com
I'll put everything I need to memorize for my math classes in this cheat sheet. It includes things from basic algebra, to limits, to derivatives and finally integrals.
This is a draft cheat sheet. It is a work in progress and is not finished yet.
Derivatives
Expression |
Derivative |
f(x)=k |
f'(x)=0 |
f(x)=x |
f'(x)=1 |
f(x)=xa |
f'(x)=axa-1 |
f(x)=ax |
f'(x)=ax lna |
f(x)=kx |
f'(x)=k |
f(x)=1/x |
f'(x)=-1/x2 |
f(x)=ln x |
f'(x)=1/x |
f(x)=eu |
f'(x)=u'.eu |
f(x)=logaX |
f'(x)=1/x lna |
f(x)=sen(x) |
f'(x)=cos(x) |
f(x)=sec(x) |
f'(x)=sec(x).tan(x) |
f(x)=arcsen(x) |
f'(x)=1/√1-x2 |
f(x)=cos(x) |
f'(x)=-sen(x) |
f(x)=csc(x) |
f'(x)=-csc(x).ctg(x) |
f(x)=arccos(x) |
f'(x)=-1/√1-x2 |
f(x)=tan(x) |
f'(x)=sec2(x) |
f(x)=ctg(x) |
f'(x)=-csc2(x) |
f(x)=arctan(x) |
f'(x)=1/1+x2 |
Integrals
∫xkdx |
(xk+1)/(k+1) + C |
∫x-1dx |
ln|x| + C |
∫dx |
x + C |
∫kF(x)dx |
k∫F(x)dx |
∫[F(x)±∫G(x)] |
∫F(x)dx ± ∫G(x)dx |
∫ekxdx |
(1/k)ekx + C |
∫akxdx |
akx/[kLn(a)] + C |
∫sen(kx) dx |
-(1/k) cos(kx) + C |
∫cos(kx) dx |
1/k sen(kx) + C |
∫sec(kx) dx |
1/k(Ln|sec(kx) + tan(kx)|) + C |
∫Tan(kx) dx |
-(1/k) Ln|cos(kx)| + C |
∫csc(kx) dx |
1/k Ln |csc(kx) - cot(kx)| + C |
∫cot(kx) dx |
1/k Ln |sen(kx)| + C |
∫sec(kx) dx |
1/k sec(kx) + C |
∫csc(kx) cot(kx) dx |
-1/k csc(kx) + C |
∫sex2(kx) dx |
1/k tan(kx) + C |
∫csc2(kx) dx |
-1/k cot(kx) + C |
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Factoring
(a + b)2 |
a2 + 2ab + b2 |
(a - b)2 |
a2 - 2ab + b2 |
a2 - b2 |
(a - b) (a + b) |
(a + b)3 |
a3 + 3a2b + 3ab2 + b3 |
(a - b)3 |
a3 - 3a2b + 3ab2 - b3 |
a3 - b3 |
(a - b)^3 + 3ab (a - b) |
a3 + b3 |
(a + b)3 - 3a b (a + b) |
Factoring
Given x^2+ax+b=0, then you have to find two numbers that when multiplied give you B and added give you a.
Example:
x^2+4x+3, turns into: (x+3)(x+1) |
Absolute value propertie
|x|>a |
x>a or a<-a |
|x|<a |
-a<x<a |
Logs properties
logaBn |
nlogaB |
logaA=lne |
1 |
loga1=ln1 |
0 |
loga(m.n) |
logaM + logaN |
loga(m/n) |
logaM - logaM |
Exponential properties
a0 |
1 |
a1 |
a |
am . an |
am+n |
am / an |
am-n |
(a.b)n |
an . bn |
(a/b)n |
an/bn |
(am)n |
am.n |
an/m |
raiz m de an |
a-1 |
1/a |
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Trigonometrical identities
sen² α + cos² α = 1 |
sec² α = 1 + tg² α |
cosec² α = 1 + cotg² α |
tan α = senα/cosα |
tan² α +1 = sec² α |
cot² α +1 = csc² α |
sin(x + y) = sin(x) cos(y) + cos(x) sin(y) |
cos(x + y) = cos(x) cos(y) − sin(x) sin(y) |
tan(x + y) = (tan(x) + tan(y))/(1 − tan(x) tan(y)) |
sin(x − y) = sin(x) cos(y) − cos(x) sin(y) |
cos(x − y) = cos(x) cos(y) + sin(x) sin(y) |
tan(x − y) = (tan(x) − tan(y))/(1 + tan(x) tan(y)) |
sin (2 x) = 2 sin (x) cos (x) |
cos (2 x) = cos2 (x) − sin2 (x) |
cos (2 x) = 2 cos2 (x) − 1 |
tan (2 x) = (2 tan (x))/(1 − tan2 (x)) |
sin2 (x) = 1/2 (1 − cos (2 x)) |
cos2 (x) = 1/2 (1 + cos (2 x)) |
sin (x) cos (x) = 1/2 sin (2 x) |
sin (x) sin (y) = 1/2 (cos (x − y) − cos (x + y)) |
sin (x) cos (y) = 1/2 (sin (x − y) + sin (x + y)) |
cos (x) cos (y) = 1/2 (cos (x − y) + cos (x + y)) |
csc(x) = 1/sin(x) |
sec(x) = 1/cos(x) |
cot(x) = cos(x)/tan(x) |
sin(−x) = − sin(x) |
cos(−x) = cos(x) |
tan(−x) = − tan(x) |
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