已知y=cos(x+y),求dy

谁知道啊,请详细一下,谢谢了
2024-11-18 10:56:23
推荐回答(3个)
回答(1):

y’=-(x+y)’sin(x+y)=-(1+y’)sin(x+y)
得y'[1+sin(x+y)]=-sin(x+y)
y'=-sin(x+y)/[1+sin(x+y)]

所以dy=-sin(x+y)/[1+sin(x+y)]dx

回答(2):

dy=d(cos(x+y))
dy=-sin(x+y)d(x+y)
dy+sin(x+y)(dx+dy)=0
(1+sin(x+y))dy=-sin(x+y)dx
dy=-sin(x+y)dx/(1+sin(x+y))

回答(3):

两边同时对X求导
dy/dx=-sin(x+y)(1+dy/dx)
就可以啦