Question

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

Answer 1

`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))`.