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33 Cards in this Set

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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^a-b
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^(n-1) * 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