How do you differentiate #2xln(x-y)-e^(x-y)#?

1 Answer
Dec 28, 2015

#dy/dx=((2x)/(x-y)+2ln(x-y)-e^(x-y))/(1-(2x)/(x-y)+e^(x-y))#.

Explanation:

I assume that y is a function of x.
Since you cannot obtain y explicitly as a function of x, you would have to use the method of implicit differentiation here, at all times bearing in mind that y is a function of x.

#therefore d/dx(y)=d/dx(2xln(x-y)-e^(x-y))#

#therefore dy/dx=2x * 1/(x-y) * (1-dy/dx)+2ln(x-y)-e^(x-y) * (1-dy/dx)#

#thereforedy/dx(1-(2x)/(x-y)+e^(x-y))=(2x)/(x-y)+2ln(x-y)-e^(x-y)#

#therefore dy/dx=((2x)/(x-y)+2ln(x-y)-e^(x-y))/(1-(2x)/(x-y)+e^(x-y))#.