Dérivées : formulaire

Dérivées : formulaire
Formules générales
(f (x) ± g(x))0 = f (x)0 ± g(x)0
(f (x).g(x))0 = f (x)0 g(x) + f (x)g(x)0
0
f (x)0 g(x) − f (x)g(x)0
f (x)
=
g(x)
g(x)2
(kf (x))0 = kf (x)0
Formules particulières
(k)0 = 0
(x)0 = 1
(xn )0 = nxn−1
√ 0
1
( x) = √
2 x
0
1
1
=− 2
x
x
(f (x)n )0 = nf (x)n−1 f (x)0
p
0
f (x)0
f (x) = p
2 f (x)
0
1
f (x)0
=− 2
f (x)
f (x)
(cos x)0 = − sin x
(sin x)0 = cos x
(cos f (x))0 = − sin f (x)f (x)0
(sin f (x))0 = cos f (x)f (x)0
1
cos2 x
1
(cot x)0 = − 2
sin x
f (x)0
cos2 f
f (x)0
0
(cot f (x)) = − 2
sin f
(tan x)0 =
(tan f (x))0 =
1
1 − x2
1
(arccos x)0 = − √
1 − x2
f (x)0
p
(arcsin f (x)) =
1 − f 2 (x)
f (x)0
(arccos f (x))0 = − p
1 − f 2 (x)
0
(arcsin x) = √
(arctan x)0 =
(ln x)0 =
1
1 + x2
1
x
(loga x)0 =
0
(arctan f (x))0 =
f (x)0
1 + f 2 (x)
f (x)0
f (x)
f (x)0
(loga f (x))0 =
f (x). ln a
(ln f (x))0 =
1
x. ln a
(ex )0 = ex
(ef (x) )0 = ef (x) .f (x)0
(ax )0 = ax . ln a
(af (x) )0 = af (x) . ln a.f (x)0