Question

What is the implicit derivative of `4= xyln(x-y)`?

Answer 1

`dy/dx=(yln(x-y)+(xy)/(x-y))/((xy)/(x-y)-xln(x-y))`

Explanation:

`4=xyln(x-y)`

`0=yln(x-y)+(xy)/(x-y)+xln(x-y)dy/dx-(xy)/(x-y) dy/dx`

`(xy)/(x-y) dy/dx-xln(x-y)dy/dx=yln(x-y)+(xy)/(x-y)`

`((xy)/(x-y)-xln(x-y))dy/dx = yln(x-y)+(xy)/(x-y)`

`dy/dx=(yln(x-y)+(xy)/(x-y))/((xy)/(x-y)-xln(x-y))`