`x e^y = x - y` Find `(dy/dx)` by implicit differentiation.

Note:- 1) If y = e^x
; then dy/dx = e^x

2) If y
= x^n ; then dy/dx = n*x^(n-1) ; where 'n' = real number

3) If y = u*v ; where both u & v are functions of 'x' ;
then 

dy/dx = u*(dv/dx) +
v*(du/dx)

Now, the given function is :-

x*(e^y) = x - y

Differentiating both sides w.r.t 'x' we
get

x*(e^y)*(dy/dx) + (e^y) = 1 + (dy/dx)

or, [x*(e^y) -
1]*(dy/dx) = [1 - (e^y)]

or, dy/dx = [1 - (e^y)]/[x*(e^y) -
1]