take x^y=u
e^(x-y)=v
both are equal so du/dx=dv/dx
find du/dx & dv/dx separately by taking log and equate them,take dy/dx on one side .this is your answer.
log u=logx^y
differentiate both sides
log u=ylogx
(1/u)du/dx=(dy/dx)logx + y/x
du/dx= [ (dy/dx)logx + y/x]x^y ,bringing u this side and keeping its value
now finding dv/dx
logv=(x-y)loge
(1/v)dv/dx=(1-dy/dx)(1/e)
dv/dx=[(1-dy/dx)(1/e)]e^(x-y)
put
du/dx = dv/dx
and get the answer