I'm trying to differentiate an implicit expression
$x e^{y} = x -y$
This is my sagemath code
x = var('x')
f(x,y)= x*e**y - x + y
show(diff(f))
Sagemath Answer is $\left( x, y \right) \ {\mapsto} \ \left(e^{y} - 1,\,x e^{y} + 1\right)$
But the actual answer is $\frac{1 - e^{y}}{x e^{y} + 1}$
How do I get the actual answer using sagemath?
