ysinx-cos(x+y)=0,求 dy/dx
问题描述:
ysinx-cos(x+y)=0,求 dy/dx
答
应用复合函数求导方法,
y′sinx+ycosx+(1+y′)sin(x+y)=0,
(sinx+sin(x+y))y′+ycosx+sin(x+y)=0,
y′=-(ycosx+sin(x+y))/(sinx+sin(x+y)).
故 dy/dx=y′=-(ycosx+sin(x+y))/(sinx+sin(x+y)).