How do you implicitly differentiate #ln(x-y)=x-y #?

1 Answer
Jun 11, 2016

It appears as if there is no solution.

Explanation:

Since we cannot get y explicitly as a function of x, we use implicit differentiation.

Differentiate both sides, bearing in mind that y is a function of x, and then solve for #dy/dx#.

#therefore d/dxln(x-y)=d/dx(x-y)#

#therefore1/(x-y)*(1-(dy)/dx)=1-(dy)/dx#

#therefore(dy)/dx(1/(x-y)-1)=(1/(x-y)-1)#

This seems to indicate the impossible fact of #(dy)/dx=1# for if this is true then #y=intdx=x# and we cannot divide by zero, nor take the natural logarithm of zero.

Hence there is no solution.