设y=f(x-y)其中f可导且f'≠1则dy/dx=?_数学解答

设y=f(x-y)其中f可导且f'≠1则dy/dx=?

人气：310 ℃　时间：2019-10-09 12:23:02

解答

y=f(x-y)
dy/dx=f'(x-y)*d(x-y)
=f'(x-y)*(1-dy/dx)
=f'(x-y)-f'(x-y)*dy/dx
[1+f'(x-y)]dy/dx=f'(x-y)
dy/dx=f'(x-y)/[1+f'(x-y)]