D´ eriv´ ees usuelles
Fonction D´eriv´ee
f(x) =k f�(x) = 0 k∈R; x∈R
f(x) =x f�(x) = 1 x∈R
f(x) =xn f�(x) =nxn−1 n∈Z∗ ; x∈Rou R∗ si n�−1 f(x) = 1
x f�(x) =− 1
x2 x∈R∗ f(x) =√
x f�(x) = 1
2√
x x∈ ]0; +∞[ f(x) = ln(x) f�(x) = 1
x x∈ ]0; +∞[
f(x) = ex f�(x) = ex x∈R
Op´ erations
Fonction D´eriv´ee
f =U +V f� =U�+V�
f =kU f� =kU� k∈R
f =U V f� =U V�+U�V f = U
V f� = V U�−U V�
V2 V(x)�= 0
f = 1
V f� = −V�
V2 V(x)�= 0
f =Un f� =nU�Un−1 n∈N∗
f =√
U f� = U�
2√
U U(x)>0
f = ln(U) f� = U�
U U(x)>0
f = exp(U) = eU f� =U�exp(U) =U�eU f(x) =V ◦U(x) f�(x) =U�(x)×V�(U(x))
