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

1.	If`e^x+e^y=e^(x+y),` prove that `(dy)/(dx)+e^(y-x)=0`
Answer» Given : `e^(x)+e^(y)=e^(x+y)." …(i)"` On dividing throughout by `e^(x+y)`, we get `e^(-y)+e^(-x)=1." …(ii)"` `e^(-y).((-dy)/(dx))+e^(-x)(-1)=0` `rArr(dy)/(dx)=(-e^(-x))/(e^(-y))=-e^((y-x)).`

Discussion

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