Cheatography

# Algebra, Calculus I & II Cheat Sheet (DRAFT) by pablocdch

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

### 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|

### Divisions with 0

 0/n 0 n/∞ 0 n/0 ∞

### 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

### 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)