e^x+e^y = (e^x)(e^y), dy/dx = -e^(y-x) how to get this?

[xeonph]

my book has this problem e^x+e^y = (e^x)(e^y) and together with it is its dy/dx = -e^(y-x), i need the solution on how to get this answer, thanks!

 

[Ishuda]

my book has this problem e^x+e^y = (e^x)(e^y) and together with it is its dy/dx = -e^(y-x), i need the solution on how to get this answer, thanks!

Take the derivative wrt x of the function
f(x,y) = e^x + e^y - e^x+y = 0
Then substitute for e^x - e^x+y and e^y - e^x+y and simplify.