Confusion with Partial Derivatives: Why does y disappear? | Explained

[bobsmith76]

Homework Statement

I don't understand why

∂f/∂x = xy = y

whereas

∂f/∂x = x² + y² = 2x

Why does the y disappear in the second but not in the first?

 

[tiny-tim]

hi bobsmith76!

you mean? …

∂/∂x (xy) = y

∂/∂x (x² + y²) = 2x​

in each case, y is treated as a constant

in the first, it's multiplied, so it stays; in the second, it's on its own, so its derivative is zero

∂/∂x means differentiating wrt x while keeping all other variables constant​