I am asked to take the derivative of the following equation for $y$:
$y = x + xe^y$
However, I get lost. I thought that it would be
$\begin{align} & y' = 1 + e^y + xy'e^y\\ & y'(1 - xe^y) = 1 + e^y\\ & y' = \frac{1+e^y}{1-xe^y} \end{align}$
However, the text book gives me a different answer. Can anyone help me with this?
Thank you and sorry if I got any terms wrong, my math studies were not done in English... :)