If e^x - e^y = x + y, then y^' = ............(possible solutions below)...?

Question

a. (e^x - 1)/ (e^y + 1)
b. (1 + e^x)/ (1 - e^y)
c. (1 - e^x) /(e^y - 1)
d. (1 - e^x) /(1 + e^y)
e. (1 + e^x)/ (1 + e^y)
f. none of these

Answer 1

differentiate e^x - e^y = x + y with respect to x:
e^x -e^y y' = 1+y'
y'(1 +e^y) = e^x -1
y'= (e^x -1) / (1 +e^y)
so the correct answer is a. .

Answer 2

It's an exercise in implicit differentiation.

(e^x)' = e^x
(e^y)' = (e^y) * y'
(x)' = 1
(y)' = y'

So taking the derivative, with respect to x of the above equation,

e^x - y' * e^y = 1 + y'

You should be able to take it from here...

Answer 3

f