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?
Why does y disappear when taking ∂f/∂x of x² + y²?
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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?
Discussion
Science Advisor
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hi bobsmith76! 
you mean? …
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
you mean? …
∂/∂x (xy) = y
∂/∂x (x2 + y2) = 2x
∂/∂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