xsiny + ycosx = 3

I'll write dy/dx as y'

Differentiating (Using Product Rule)

siny + xy'cosy + y'cosx - y sinx = 0

y'(x cosy + cos x) = y sinx - siny

y' = y sinx - siny / (x cosy + cos x)

xsiny + ycosx = 3 let dy/dx be y'so y'(xcosy + cosx) = y sinx - siny   so y' = (ysinx-siny)/(xcosy+cosx)

 for such functions check out this shortcut :

let f = xsiny+ycosx-3

dy/dx  =    where  indicates partial derivative .

if u plug in the value of f as given above and differentiate u can find ans to such long problems in split seconds.....

dy/dx = - (siny -y sinx) / (xcos y+ cos x)

u can try the same formula for things like x tany etc.

rate if u find useful