if `e^(x+y)=x y ,` show that `(dy)/(dx)=(y(1-x))/(x(y-1))`

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

If x^(y)=e^(x-y), show that (dy)/(dx)=(y(x-y))/(x^(2))

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

If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)) .

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

If y=e^(x-y) then show that (dy)/(dx) = y/(1+y)

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

If e^x+e^y = e^(x+y) , show that (dy)/(dx) = -e^(y-x)

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

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