Let u=yx,v=xy,w=xx
(i)u=yx⇒log u=x log y ⇒dudx=yx[log y+xydydx]
(ii)v=xy⇒log v=y log x ⇒dvdx=xy[log xdydx+yx]
(iii)w=xx⇒log w=x log x ⇒dwdx=xx[log x+1]
Now yx+xy+xx=ab ⇒u+v+w=ab ⇒dudx+dvdx+dwdx=0
⇒yx[log y+xydydx]+xy[log xdydx+yx]+xx[log x+1]=0
∴ dydx=−yxlog y+yxy−1+xx[log x+1]log x+x yx−1=0