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

bobsmith76
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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?
 
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hi bobsmith76! :wink:

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 :smile:

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

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