If `y=log(e^(m x k)+e^(-m x k))` then prove that `(dy)/(dx)=mk[(e^(mxk)-1)/(e^(2mxk)+1)]`

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

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

if x^(y)=e^(x-y) then prove that (dy)/(dx)=(log_(e)x)/((1+log_(e)x)^(2))

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

If x^(y)=e^(x-y) then prove that (dy)/(dx)=(ln x)/((1+ln x)^(2))

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

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

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

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