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

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

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

If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)) .

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

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

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

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2) If y=sin(2sin^(-1)x), show that ((1-x^(2))d^(2y))/(dx^(2))=x(dy)/(dx)-4y

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