1 / 25

第四节 多元复合函数的求导法则 - PowerPoint PPT Presentation

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' 第四节 多元复合函数的求导法则' - keiki

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

1.复合函数的中间变量均为一元函数的情形.

z=f[φ(t),ψ(t),ω(t)]则在与定理类似的条件下,这函数在

2. 复合函数的中间变量均为多元函数 的情形

u=φ(x,y),v=ψ(x,y) 实际上都是x,y的二元函数,因此要把(1)中

w=ω(x,y) 都具有偏导数,则复合函数z=f[φ(x,y),ψ(x,y),ω(x,y)]

3.复合函数的中间变量即有一元函数,又有多元函数的情形3.复合函数的中间变量即有一元函数,又有多元函数的情形

v与x无关

;在v对y求导时,由于v是y的一元函数,故

z=f[φ(x,y),x,y]

x

z---u

y

x

u

z

x

x

y

z

u

v

w

x

y

u

v

x

z

x

y

u

v

x

z

(1)用图示法表示出函数的复合关系. 如

(2)函数对某自变量的偏导数之结构

1).项数=中间变量个数 (u,v,x)3个→三项.

2).每一项=函数对中间变量的偏导数×该中间变量对其指

(3)一般情况,函数z对中间变量u,v,w的偏导数

(4)对于抽象函数在求偏导数时,一定要设中间变量.例如

u

x

z

v

y

.

v=xy