(dy)/(dx)=(y(x-y^(2)-y))/(x(x ln x-y))

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

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

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

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

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

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

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

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