formulas Flashcards
integral sec x tan x dx=
sec x+C
integral 0 dx=
C
integral 1 dx=
x+C
integral e x dx=
e x+C
integral 1/x dx=
ln x+C
integral n^xdx
n^x / ln x+C
integral cos x dx=
sin x+C
integral sin x dx=
_cos x+C
integral sec^2 x dx=
tan x+C
integral csc^2 x dx=
_cot x+C
integral sec x tan x dx=
sec x+C
integral csc x cot x dx=
_csc x+C
d/dx ln x
1/x
d/dx sinh u=
cosh u
d/dx cosh u=
sinh u
d/dx tanh u=
Sech^2 u
integral sinhu du=
cosh u + C
integral cosh u du=
sinh u + C
integral sech^2 u du=
tanh u + C
integral csch^2 u du=
-coth u + C
integral sech u tanh u du=
-sech u + C
integral csch u coth u du=
-csch u + C
d/dx coth u=
-csch^2 u
d/dx sech u =
-sech u tanh u
d/dx csch u =
-csch u coth u
d/dx of ln(x)=
1/x
d/dx ln ( f(x) ) =
1/f(x) (fâ(x))
d/dx loga(X)=
1/xlna
d/dx log a (f(x))=
1/(f(x) lna )
product rule g(f(x))=
gâf x fâg
Chain rule
getting the derivative of out side and leave inside alone and then multiplying by the derivative of inside
you an write the square root of X as X to the power 1/2, how about ln of square root of X
ln of square root of x we can rewrite as ln of x to the power 1/2 and then rewrite as 1/2lnx
ln (abcd)=
(lna)(lnb)(lnc)(lnd)
Log a (x)=y
a^y=x
loga (xy)=
loga (x) + loga (y)
loga (x/y)=
loga (x) - loga (y)
loga (a^x)=
x
lnx=e then e^lnx=e^e
x=e^e
change base formula
loga (b) = ln(b) / ln(a) remember base goes to the basement (bottom)
d/dx a^x=
a^x lna
d/dx a^x=
a^x lna
d/dx a^f(x)
a^f(x) lna fâ(x)
d/dx of ln(x)=
1/x
d/dx ln ( f(x) ) =
1/f(x) (fâ(x))
d/dx loga(X)=
1/xlna
d/dx log a (f(x))=
1/(f(x) lna )
product rule g(f(x))=
gâf x fâg
Chain rule
getting the derivative of out side and leave inside alone and then multiplying by the derivative of inside
you an write the square root of X as X to the power 1/2, how about ln of square root of X
ln of square root of x we can rewrite as ln of x to the power 1/2 and then rewrite as 1/2lnx
ln (abcd)=
(lna)(lnb)(lnc)(lnd)
Log a (x)=y
a^y=x
loga (xy)=
loga (x) + loga (y)
loga (x/y)=
loga (x) - loga (y)
loga (a^x)=
x
lnx=e then e^lnx=e^e
x=e^e
change base formula
loga (b) = ln(b) / ln(a) remember base goes to the basement (bottom)
d/dx a^x=
a^x lna
d/dx a^x=
a^x lna
d/dx a^f(x)
a^f(x) lna fâ(x)
Half life
Ln2/k or Ln0.5/k
Decay and growth
A(t)=A0e^rt Y=Y0e^kt R is the interest or percent T is number of years A0 is initial value
Temp formula
T-Ts=(T0-Ts)e^-kt T is the current temp or the one we want to get to and Ts is the room temp and T0 is the initial temp
Hyperbolic sinh
(e^x - e^-x) / 2
Hyperbolic cosh
(e^x + e^-x) / 2
Cosh^2x - sinh^2x=
1
Sinh2x
2sinhx
what do we use if we have squer root of (a2 - X2)
then we put X= a sin
what do we use if we have squer root of (a2 + X2)
then we put X=a tan Ă
what do we use if we have squer root of (X2 - a2)
then we put X = a Sec
sin2X=
2 sinX cosX
integral of Sec X dx=
ln I secx+tanx I + c
integral of Csc x dx=
ln I csc x - cot x I + c
Sec2X - 1
tan2X
integral of (tan x) dx=
ln I sec x I + c
integral of Sec X dx=
ln I sec x + tan x I + c
Cos 2X =
1/2 ( 1 + cos (2x))
sin2X=
1/2 ( 1 - cos (2x))
1+ tan2X =
sec2X
integral of sin (mx) Cos (nx) dx=
we have to use Sine A Cos B =
1/2 [sin (A-B) + sin ( A+B)]
integral of sin (mx) sin (nx) dx=
we have to use Sine A sin B =
1/2 [cos (A-B) - cos ( A+B)]
integral of cos (mx) Cos (nx) dx=
we have to use cos A Cos B =
1/2 [cos (A-B) + cos (A+B)]
