*Note:- 1) If y = sinx ; then dy/dx = cosx *

*2) If y = e^x ; then dy/dx = e^x*

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

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

*4) If y = x^n ; where 'k' = constant ; then dy/dx = n*x^(n-1)*

Now, the given function is :-

(e^y)*sinx = x + xy

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

(e^y)*cosx + {(e^y)*sinx}*(dy/dx) = 1 + y + x*(dy/dx)

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

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