SOLUTION: what is the solution to: implicit differentiation e^x + e^y = e^x+y

Question 765940: what is the solution to:
implicit differentiation
e^x + e^y = e^x+y
Answer by MaartenRU(13) (Show Source): You can put this solution on YOUR website!
I will assume you mean , and not , because that would require , which has no real solution.

Alright, we now have

We will first substitute :

Now we want to separate u from the rest of the equation.

Factor out u:

So putting the substitution back gives us

And so:

Of course this requires that the denominator is not zero, which translates to x not equal to zero. For any other x, this is the y that satisfies the equation.
RELATED QUESTIONS
Please find dy/dx using implicit differentiation: y^2+e^y=ln x^2+4... (answered by funmath)

Let {{{ e^(xy) = 4x+4y+20 }}} Use implicit differentiation to find the derivative of y (answered by Fombitz)

Can you help me with this problem? Solve by means of implicit differentiation: (e^x)... (answered by solver91311,rothauserc)

Use implicit differentiation to find dy/dx: e^y lnx+ xy3=... (answered by venugopalramana)

Use the logarithmic differentiation to differentiate the function y= (x+2)^2/(e^x... (answered by Alan3354)

Differentiate using implicit differentiation. a. x^2+y^2=9 (answered by Solver92311)

Differentiation Differentiate... (answered by Fombitz)