**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]

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