الداله f ( x ) = {\displaystyle f(x)=\,}
المشتقه f ′ ( x ) = {\displaystyle f'(x)=\,}
شرط الاشتقاق
a {\displaystyle a\,\!}
0 {\displaystyle 0\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }
a x {\displaystyle ax\,\!}
a {\displaystyle a\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }
1 x {\displaystyle 1 \over x\,\!}
− 1 x 2 {\displaystyle -{1 \over x^{2}}\,\!}
x ∈ R ∗ {\displaystyle x\,\in \mathbb {R} ^{*}}
x {\displaystyle {\sqrt {x}}\,\!}
1 2 x {\displaystyle {1 \over 2{\sqrt {x}}}\,\!}
x ∈ R + ∗ {\displaystyle x\,\in \mathbb {R} _{+}^{*}}
a x n {\displaystyle ax^{n}\,\!}
a n x n − 1 {\displaystyle anx^{n-1}\,\!}
n ∈ N ∗ x ∈ R {\displaystyle n\,\in \mathbb {N} ^{*}\quad x\,\in \mathbb {R} }
a x n {\displaystyle ax^{n}\,\!}
a n x n − 1 {\displaystyle anx^{n-1}\,\!}
n ∈ Z ∖ N x ∈ R ∗ {\displaystyle n\,\in \mathbb {Z} \setminus \mathbb {N} \quad x\,\in \mathbb {R} ^{*}}
a x c {\displaystyle ax^{c}\,\!}
a c x c − 1 {\displaystyle acx^{c-1}\,\!}
c ∈ R ∖ Z x ∈ R ∗ + {\displaystyle c\,\in \mathbb {R} \setminus \mathbb {Z} \quad x\,\in \mathbb {R} ^{*+}}
cos ( x ) {\displaystyle \cos(x)\,\!}
− sin ( x ) {\displaystyle -\sin(x)\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }
sin ( x ) {\displaystyle \sin(x)\,\!}
cos ( x ) {\displaystyle \cos(x)\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }
tan ( x ) {\displaystyle \tan(x)\,\!}
1 cos 2 ( x ) {\displaystyle 1 \over \cos ^{2}(x)} ou 1 + tan 2 ( x ) {\displaystyle 1+\tan ^{2}(x)\,\!}
x ≠ π 2 + k π {\displaystyle x\neq {\pi \over 2}+k\pi } , k ∈ Z {\displaystyle k\in \mathbb {Z} }
arccos ( x ) {\displaystyle \arccos(x)\,\!}
− 1 1 − x 2 {\displaystyle -{1 \over {\sqrt {1-x^{2}}}}\,\!}
x ∈ ] − 1 ; 1 [ {\displaystyle x\,\in \ ]-1;1[}
arcsin ( x ) {\displaystyle \arcsin(x)\,\!}
1 1 − x 2 {\displaystyle {1 \over {\sqrt {1-x^{2}}}}\,\!}
x ∈ ] − 1 ; 1 [ {\displaystyle x\,\in \ ]-1;1[}
arctan ( x ) {\displaystyle \arctan(x)\,\!}
1 1 + x 2 {\displaystyle {1 \over 1+x^{2}}\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }
a x {\displaystyle a^{x}\,\!}
a x ln a {\displaystyle a^{x}\ln a\,\!}
a ∈ R + ∗ x ∈ R {\displaystyle a\,\in \mathbb {R} _{+}^{*}\quad x\,\in \mathbb {R} }
ln | x | {\displaystyle \ln |x|\,\!}
1 x {\displaystyle 1 \over x\,\!}
x ∈ R ∗ {\displaystyle x\,\in \mathbb {R} ^{*}}
exp x {\displaystyle \exp {x}\,\!}
exp x {\displaystyle \exp {x}\,\!}
x ∈ R {\displaystyle x\,\in \mathbb {R} }