Question

隐函数。。极难。。高分啊

设Y=Y(X)由方程YSINX-SIN(X+Y)=0所确定。。求Y的隐函数导数~？

Answer 1

YSINX-SIN(X+Y)=0
ysinx=sin(x+y)
两边分别对x进行求导
得到y'sinx+ycosx=(1+y')cos(x+y)
y'[sinx-cos（x+y)]=cos(x+y)-ycosx
=cos(x+y)-sin(x+y)cosx/sinx
=[sinx*cos(x+y)-sin(x+y)*cosx]/sinx
=sin(x-x-y)/sinx=-1
得到y'=1/[cos（x+y）-sinx]

Answer 2

点击看大图

Answer 3

不难啊，两边对x求导，注意y是x的函数，用复合函数求导法则就可以，课本的内容啊

Answer 4

y'sinx+ycosx=cos(x+y)(1+y')
y'sinx-y'cos(x+y)=cos(x+y)-ycosx
y'=[cos(x+y)-ycosx]/[sinx-cos(x+y)]

Answer 5

y'sinx+ycosx-cos(x+y)(y'+1)=0
y'=[cos(x+y)-ycosx]/[sinx-cos(x+y)]