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
答
【cos(x+y)-y】/【x-cos(x+y)】
答
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)]
答
(cos(x+y)-y)\(x-cos(x+y))