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)}
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} }
![{\displaystyle x\,\in \ ]-1;1[}](https://wikimedia.org/api/rest_v1/media/math/render/svg/373521c9bc0880182a30ed3bfb80925141a1f3f6)
