What is the derivative for e^(x+y) = y?

Question

What is dy/dx for e^(x+y) =y

Answer 1

Use implicit differentiation.  Differentiate both sides of the equation using the chain rule.

 

(1 + y')e^{(x + y)} = y'

 

e^{(x + y)} + e^{(x + y)}y' = y'

 

 

Now we isolate all the y' terms.

 

e^{(x + y)}y' - y' = -e^{(x + y)}

 

 

Factor out y'.

 

y' [e^{(x + y)} - 1] = -e^{(x + y)}

 

 

Divide both sides of the equation by  (e^{(x + y)} - 1).