求全套的求导公式
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求全套的求导公式
![求全套的求导公式](/uploads/image/z/17807227-43-7.jpg?t=%E6%B1%82%E5%85%A8%E5%A5%97%E7%9A%84%E6%B1%82%E5%AF%BC%E5%85%AC%E5%BC%8F)
复合函数求导
F'(g(x)) = [ F(g(x+dx)) - F(g(x)) ] / dx (1)
g(x+dx) - g(x) = g'(x)*dx = dg(x) (2)
g(x+dx) = g(x) + dg(x) (3)
F'(g(x)) = [ F(g(x) + dg(x)) - F(g(x)) ] /dx =
[ F(g(x) + dg(x)) - F(g(x)) ] / dg(x) * dg(x)/dx =
F'(g) * g'(x)
基本函数的求导公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/√1-x^2
10.y=arccosx y'=-1/√1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x
![](http://img.wesiedu.com/upload/5/6b/56b19455e6948e059d360d3ab5616d65.jpg)
F'(g(x)) = [ F(g(x+dx)) - F(g(x)) ] / dx (1)
g(x+dx) - g(x) = g'(x)*dx = dg(x) (2)
g(x+dx) = g(x) + dg(x) (3)
F'(g(x)) = [ F(g(x) + dg(x)) - F(g(x)) ] /dx =
[ F(g(x) + dg(x)) - F(g(x)) ] / dg(x) * dg(x)/dx =
F'(g) * g'(x)
基本函数的求导公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/√1-x^2
10.y=arccosx y'=-1/√1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x
![](http://img.wesiedu.com/upload/5/6b/56b19455e6948e059d360d3ab5616d65.jpg)