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29 Cards in this Set
 Front
 Back
Differentiation d/dx sin x = 
cos x 

Differentiation d/dx cos x 
sinx 

Differentiation f'n = 1+sinxcosx 
= cos x + sin x 

tan x 
= sin x /cos x 

Product Rule 
y' = Vu' + Uv' where u = 1st Bracket v = 2nd Bracket 

Quotient Rule 
y' = (Vu'  Uv')/ V^2 where u = top part v = bottom part 

Chain Rule 
dy/dx = dy/du x du/dy 

Pythagorus Theorem 
y' = (Cos2 x + sin2 x)/ cos2 x = 1/cos2 x 

AntiDifferentiation { cos 4/3 x dx 
= 3/4 sin 4/3x + c 

AntiDifferentiation y' = 3 sin 1/2 x 
y =  6 cos 1/2 x + c 

AntiDifferentiation or Integration Cycle 
sin > cos > sin > cos > sin 

Differentiation Cycle 
sin > cos > sin >  cos > sin 

Trapezoidal Rule: Width of each strip 
(ba)/ n 

Trapezoidal Rule: Length of Integral 
b  a 

Bernoulli Trial : 
There are only two possible answers  as long as trials are independent 

Bernoulli Trial : Equation 
p(success) + q(failure) = 1 

Bernoulli Trial : Equation 2 
^n Cx . p^x . q ^nx 

Exponential and Log Functions: EQUATIONS 
y= a^x log,a, y = x 

Exponential and Log Functions: Q1 = 32 ^ 3/5 
= (2^5)^3/5 =  2^3 =  8 

Exponential and Log Functions: Q2  3^x = 243 
Let 3^x = 3^5 Then x = 5 

Exponential and Log Functions: Q3  3^x = 15 
(log15)/log 3 = 2.46 to 2.d.p 

Laws and Properties: = Log xy 
= Log x + Log y 

Laws and Properties: Log x^n 
= n Log x 

Laws and Properties: log 1 
= 0 

Laws and Properties: log 10 
= 1 

Laws and Properties: 10 ^ logx 
= x 

Laws and Properties: Log,a, x = log,a, y 
> x = y 

Euler's Number: 
f(x) = a^x, aER (Cannot Equal) 1
e = lim ( 1  1/n)^n n> Infinity 

Euler's Number: Q1  5^2x = e^y 
log,e, 5^2x = log,e, e^y 2x log,e, 5 = y log,e, e 2x log,e, 5 = y 2x . 1.6094 = y 3.219x = y 