设函数y=f(x),由方程xy-sin(x+y)=0,确定dy/dx

问题描述:

设函数y=f(x),由方程xy-sin(x+y)=0,确定dy/dx

【cos(x+y)-y】/【x-cos(x+y)】

xy-sin(x+y)=0
y+xy′-(1+y′)cos(x+y)=0
y+xy′-cos(x+y)-y′cos(x+y)=0
y′(x-cos(x+y))=cos(x+y)-y
y′=[cos(x+y)-y]/[x-cos(x+y)]

(cos(x+y)-y)\(x-cos(x+y))