If `x^(y) + y^(x) = a^(b)` then prove that `(dy)/(dx)=-[(yx^(y-1)+y^(x)Logy)/(x^(y)Logx+xy^(x-1))]` .

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

If y ^(x) + x ^(y) + x ^(x) = a ^(b) then find (dy)/(dx)

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

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

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

If x -y = Sin ^(-1) x - Sin ^(-1) y then (dy)/(dx) =

If x ^(y) = e ^(x -y) then (dy)/(dx) =