if xᵐyⁿ=(x+y)ᵐ⁺ⁿ prove that dy/dx=y/x
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mlogx+nlogy=(m+n)log(x+y)
m/x+n/y.dy/dx=m+n.1/x+y.(1+dy/dx)
n/y-m+n/x+y.dy/dx=m+n/x+y-m/x
nx-my/y(x+y).dy/dx=nx-my/x(x+y)
dy/dx=y/x
m/x+n/y.dy/dx=m+n.1/x+y.(1+dy/dx)
n/y-m+n/x+y.dy/dx=m+n/x+y-m/x
nx-my/y(x+y).dy/dx=nx-my/x(x+y)
dy/dx=y/x
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