I have come to a bit of a misunderstanding with partial derivatives. I will try to illustrate my problem. Say we have a function f(x, y(x), y'(x)) where y'(x)=dy/dx. Now suppose that f does not explicitly depend on x. My physics book says at this point that ∂f/∂x=0, even though y(x) and y'(x) may depend on x.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose f=y^{2}

Then ∂f/∂x=0

but if we have y(x)=x, then we can write f as:

f=x^{2}and we have

∂f/∂x=2x

How can we have two different answers for the same derivative by simply rewriting the function in a different way?

I apologize in advance if the answer is obvious and I am being a bit annoying by asking. But if you do have a helpful comment to post, I would greatly appreciate it!

-Alex

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# Simple question about partial derivatives

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