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33 Cards in this Set
 Front
 Back
derive ln(x)

1/tdt
so integral of 1/t dt = ln(x) 

ln 1 =

0


ln(ab)=

ln a + ln b


ln (a ^n)

n ln(a)


ln(a/b)

ln(a)ln(b)


e is?

the base for natural log


ln e =

1
also, integral 1/t dt from 1 to e 

derive nat log:
ln(u) 
1/u*(du/dx)
only include the du dx if the u is a chain rule and not just an x 

d/dx of ln abs(u)

u'/u


integral 1/x

ln abs (x)


integrate (1/u)

ln abs(u) + c


integral sin u

cos u +c


integral cos u

sin u + c


integral tan u

ln abs(sin u ) + c


inverse of the natural log is the

natural exponential function,
f^1(x)=e^x 

e^a*e^b=

e^a+b


e^a/e^b

e^ab


d/dx e^u

e^u*(du/dx)
only include the du/dx if the u is a chain rule, if not the e^x derives to itself. 

integral of e^u du

e^u+c


a^x=

(ln a)*a^x


loga(x)=
log base a of x 
1/(ln a)*(ln x)


d/dx (a^u)=

(ln a)*a^u *du/dx


d/dx (log a u)
derivative, log base a of u 
1/((ln a)u) * du/dx
only additional multiply for du/dx if its a chain rule 

d/dx u^n

n*u^(n1) * du/dx
only additional multiply for du/dx if its a chain rule 

inverse trig functions: input/output ?

input ratio and output angle


accoridn gto the formula sheet, the what are the formulas of the functions not given :
arcsin > arctan > arcsec > 
arccos
arccot arccsc all now include a negative u' on top. 

exponential growth and decay model

y=Ce^kt


d/dx ln(u)

u'/u


ln(0)

undefined


e^1

e


cos(0)

1


sin(0)

0


e^0

1
