´ eé

Fonction  Dérivée
f(x) = ax + b f′(x) = a
f(x) = x^{n} f′(x) = nx^{n−1}
f(x) = \sqrt{x} f′(x) = 12\sqrt{x}
f(x) = 1x f′(x) = −1x^{2}
f(x) =^{x}  f′(x) =^{x}
f(x) = ln x f′(x) = 1x
f(x) = cos x f′(x) = − sin x
f(x) = sin x f′(x) = cos x

(f + g)′ = f′ + g′ (f − g)′ = f′ − g′ (fg)′ = f′g + fg′ (\frac{f}{g})′ = \frac{f′g−fg′}{g^{2}}

Fonction Primitives
f(x) = x^{n} F (x) = 1n + 1x^{n+1} + C
f(x) = 1x F (x) = ln |x| + C
f(x) =^{x} F (x) =^{x} +C
f(x) = cos xF (x) = sin x + C
f(x) = sin xF (x) = − cos x + C

\frac{x^{2}}{a^{2}} +\frac{y^{2}}{b^{2}} −1 = 0

\frac{x^{2}}{a^{2}} −\frac{y^{2}}{b^{2}} −1 = 0

y^{2}−2px = 0

é cos^{2} x+

sin^{2} x = 1 tan x =

sin xcos x

cos(a+

b) = cos a cos b− sin a sin b cos(a−

b) = cos a cos b+ sin a sin b sin(a+

b) = sin a cos b+ sin b cos a sin(a−

b) = sin a cos b− sin b cos a sin p+ sin q = 2 sin p + q2 cos p − q2 sin p− sin q = 2 sin p − q2 cos p + q2 cos p+ cos q = 2 cos p + q2 cos p − q2 cos p− cos q =

−2 sin p + q2 sin p − q2 z = x+ y =

r(cos θ+

sin θ = r^{θ})

|z| = r =

\sqrt{x^{2} + y^{2}} arg z =

θ = arctan yx

é à é é z̄ = x− y =

r^{−θ} z+ z′ = x+ x′+ (y+

y′)

zz′ = xx′− yy′+

(xy′+ x′y) =

rr′^{(}θ+ θ′)

zz′ = zz̄′|z′|^{2} =

xx′ + yy′ + (−xy′ + x′y)x^{′2} + y^{′2} =

rr′^{(θ−θ′)} arg(z−

z′) = (Ox, mm′) |z′− z| = mm′

\overline{z + z′} = (\overline{z}+) / (\overline{z′})