Question

What is the implicit derivative of `3=x-y+xe^y`?

Answer 1

`y' = dy/dx = (1 + e^y)/(1 - x e^y)`

Explanation:

`3 = x - y + xe^y`

`0 = 1 - 1xx dy/dx + 1xxe^y + xxxdy/(dx)e^y`

`dy/dx - xxxdy/(dx)e^y = 1 + e^y`

`dy/dx (1 - x e^y) = 1 + e^y`

`dy/dx = (1 + e^y)/(1 - x e^y)`