前言
其实主要的目的是可以在文本中输出各种数学符号，便于以后用到的时候有现成的例子拿过来抄~~
常用导数公式
| 序号 | 公式 |
|---|
| 1 |
(
C
)
′
=
0
(C)'=0
(C)′=0 |
| 2 |
(
x
μ
)
′
=
μ
⋅
x
μ
−
1
(x^μ)'=μ·x^{μ-1}
(xμ)′=μ⋅xμ−1 |
| 3 |
(
s
i
n
x
)
′
=
c
o
s
x
(sinx)'=cosx
(sinx)′=cosx |
| 4 |
(
c
o
s
x
)
′
=
−
s
i
n
x
(cosx)'=-sinx
(cosx)′=−sinx |
| 5 |
(
t
a
n
x
)
′
=
s
e
c
2
x
(tanx)'=sec^2x
(tanx)′=sec2x |
| 6 |
(
c
o
t
x
)
′
=
−
c
s
c
2
x
(cotx)'=-csc^2x
(cotx)′=−csc2x |
| 7 |
(
s
e
c
x
)
′
=
s
e
c
x
⋅
t
a
n
x
(secx)'=secx·tanx
(secx)′=secx⋅tanx |
| 8 |
(
c
s
c
x
)
′
=
−
c
s
c
x
⋅
c
o
t
x
(cscx)'=-cscx·cotx
(cscx)′=−cscx⋅cotx |
| 9 |
(
a
x
)
′
=
a
x
l
n
a
(a^x)'=a^xlna
(ax)′=axlna |
| 10 |
(
e
x
)
′
=
e
x
(e^x)'=e^x
(ex)′=ex |
| 11 |
(
l
o
g
a
x
)
′
=
1
x
⋅
l
n
a
(log_ax)'=\frac{1}{x·lna}
(logax)′=x⋅lna1 |
| 12 |
(
l
n
x
)
′
=
1
x
(lnx)'=\frac{1}{x}
(lnx)′=x1 |
| 13 |
(
a
r
c
s
i
n
x
)
′
=
1
1
−
x
2
(arcsinx)'=\frac{1}{\sqrt{1-x^2}}
(arcsinx)′=1−x2
1 |
| 14 |
(
a
r
c
c
o
s
x
)
′
=
−
1
1
−
x
2
(arccosx)'=-\frac{1}{\sqrt{1-x^2}}
(arccosx)′=−1−x2
1 |
| 15 |
(
a
r
c
t
a
n
x
)
′
=
1
1
+
x
2
(arctanx)'=\frac{1}{1+x^2}
(arctanx)′=1+x21 |
| 16 |
(
a
r
c
c
o
t
x
)
′
=
−
1
1
+
x
2
(arccotx)'=-\frac{1}{1+x^2}
(arccotx)′=−1+x21 |
导数的四则运算
| 序号 | 公式 |
|---|
| 1 |
(
u
±
v
)
′
=
u
′
±
v
′
(u \pm v)'=u'\pm v'
(u±v)′=u′±v′ |
| 2 |
(
u
v
)
′
=
u
′
v
+
u
v
′
(uv)'=u'v+uv'
(uv)′=u′v+uv′ |
| 3 |
(
u
v
)
′
=
u
′
v
−
u
v
′
v
2
(
v
≠
0
)
(\frac{u}{v})'= \frac{u'v-uv'}{v^2}(v \neq 0)
(vu)′=v2u′v−uv′(v=0) |
| 4 |
(
C
u
)
′
=
C
u
′
(Cu)'=Cu'
(Cu)′=Cu′ |
| 5 |
(
C
v
)
′
=
−
C
v
′
v
2
(\frac{C}{v})'=-\frac{Cv'}{v^2}
(vC)′=−v2Cv′ |
