[" If "x=y log xy" हो,तो Prove that "],[qquad (dy)/(dx)=(y(x-y))/(x(x+y))]

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(dy)/(dx)=(y(x ln y-y))/(x(y ln x-x))

If x=y log(xy) , then prove that (dy)/(dx) = (y (x-y))/(x(x+y)) .

If x y\ log(x+y)=1 , prove that (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y)) .

If xy log(x+y)=1, prove that (dy)/(dx)=-(y(x^(2)y+x+y))/(x(xy^(2)+x+y))

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If xy=e^(x-y) , prove that (dy)/(dx)=(y(x-1))/(x(y+1)) .

If xy = e^(x - y) , prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

If x^(y)=y^(x) , prove that (dy)/(dx)=((y)/(x)-log y)/((x)/(y)-log x)

If y = x^y , prove that (dy)/(dx) = (y^2)/(x(1 - y log x))