Formules par coeur math
(cos x)'=
-sin x
(sin x)'=
cos x
(tan x)'=
1 + tan²x
(arcsin x)'=
1/ √1-x²
(arccos x)'=
-1/ √1-x²
(arctan x)'=
1/1+x²
(ch x)'=
sh x
(sh x)'=
ch x
(th x)'=
1 - th²x
ch a+b=
cha chb + sha shb
sh a+b=
sha chb + cha shb
(argsh x)'=
1/√x²+1
(argch x)'=
1/√x²-1
(argth x)'=
1/1-x²
cos a+b=
cosa cosb - sina sinb
sin a+b=
sina cosb + cosa sinb
tan a+b=
tana + tanb/1-tana tanb
tan a-b=
tana - tanb/1+tana tanb
tan π/6=
1/√3
tan π/3=
√3
tan π/4=
th a+b
tha + thb/1+tha thb
((x)^1/n)'=
(x)^1/n /nx
(1/(x)^1/n)'=
-1/nx (x)^1/n
ch 0=
sinh 0=
th 0=
argsh 0=
argch 1=
arth 0=
argth x =
1/2 ln (1+x/1-x)
argsh x =
ln (x + √x²+1)
argch x =
ln (x + √x²-1)
sin(2a)=
2sina cosa
cos(2a)=
cos²a + sin²a
tan(2a)=
2tana/1-tan²a
ch(2a)=
ch²a + sh²a = 2ch²a -1 => depuis formule d'addition
sh(2a)=
2cha sha => depuis formule d'addition
th(2a)=
2tha /th²a +1 => depuis formule d'addition
DL exp x =
1 + x + x^2/2! + x^3/3! + ... + x^n/n! + o(x^n)
DL sin x =
x - x^3/3! + x^5/5! - ... + (-1)^n x^(2n+1)/(2n+1)! + o(x^(2n+1))
DL cos x =
1 - x^2/2! + x^4/4! - ... + (-1)^n x^(2n)/(2n)! + o(x^(2n))
DL 1/1-x =
1 + x + x^2 + x^3 + ... + x^n + o(x^n)
DL 1/1+x =
1 - x + x^2 - x^3 + ... + (-1)^n x^n + o(x^n)
DL ln(1+x) =
x - x^2/2 + x^3/3 - x^4/4 + ... + (-1)^(n-1) x^n/n + o(x^n)
DL (1+x)^z =
1 + z x + z(z-1)x^2/2! + z(z-1)(z-2)x^3/3! + ... + o(x^n)
DL arctan x =
x - x^3/3 + x^5/5 - x^7/7 + ... + (-1)^n x^(2n+1)/(2n+1) + o(x^(2n+1))
DL ch x =
1 + x^2/2! + x^4/4! + ... + x^(2n)/(2n)! + o(x^(2n))
DL sh x =
x + x^3/3! + x^5/5! + ... + x^(2n+1)/(2n+1)! + o(x^(2n+1))
DL th x =
x − x^3/3 + 2x^5/15 − 17x^7/315 + ... + o(x^(2n+1))
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