Find dy/dx by implicit differentiation

Question

cos(x)e^x  = 1 + sin(xy)

Answer 1

e^x cos x = 1 + sin xy

 

e^x cos x + e^x (-sin x) = cos xy · d/dx (xy)

 

e^x (cos x - sin x) = (y + x · dy/dx) cos xy

 

y + x · dy/dx = e^x (cos x - sin x) / cos xy

 

dy/dx = e^x (cos x - sin x) / (x cos xy) - y/x