" 38.If "e^(x)+e^(y)=e^(x+y)," prove that "(dy)/(dx)+e^(y-x)=0

If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

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

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

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

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

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

if e^x+e^y=e^(x+y) then show that (dy)/(dx)+e^(y-x)=0 .