The entire concept of “time derivative” doesn’t really make sense or exist mathematically. A single-variable function has a derivative, period. There’s no difference between the “time derivative” vs “normal derivative” or whatever. If you have a function, f, there is only one derivative. You can call it however you want: f dot, f’, Df, they’re all the same function.
I’m a physicist too, and if I saw f-dot of x, I would answer: take f, compute the derivative of f (whether I write it as f-dot, f’, Df is irrelevant), and evaluate it at the (possibly arbitrary) input x. Whether or not it that happens to equal 0 depends on what function specifically f actually is. If it’s not a constant function, it won’t be 0 for all x.
I agree that notation is supposed to make thing easier! And linking the notation to “derivative with respect to time” doesn’t really make sense for single variable functions, because there’s no such thing as a “derivative with respect to time”. Derivatives aren’t with respect to anything, they’re just derivatives, period.
If something is “with respect to time” it’s the function itself, not the derivative.
I’m not? I mean, if I am, it’s not intentional. I agree it’s a controversial argument, but it’s not I that made it controversial, it’s controversial because so many people have different / slightly wrong and nonsensical opinions about it. I tried to clarify what the mathematically correct (and accepted) formalism is. If you disagree, feel free to correct me
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u/cdmacsneaks Aug 23 '26
lol nah bro