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Question

If yx+xy+xx=ab, find dydx.

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Solution

Let u=yx,v=xy,w=xx
(i)u=yxlog u=x log y dudx=yx[log y+xydydx]
(ii)v=xylog v=y log x dvdx=xy[log xdydx+yx]
(iii)w=xxlog 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+yxy1+xx[log x+1]log x+x yx1=0

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