I'm thinking in particular about Lenny Susskind's lectures, but I've seen other lecturers do it too. They'll be writing equation after equation using the partial derivative symbol:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{\partial f}{\partial a}[/itex]

And then at some point they'll realize that some problem they're currently doing is only in one variable and they'll get very embarassed, erase the partial d symbol, and replace it with an ordinary d symbol, like so:

[itex]\frac{df}{dt}[/itex]

My question is, Why does it matter? Why not just always use the partial symbol? You'd get the same result, wouldn't you? I mean, you wouldn't get a wrong answer if you used the partial symbol instead of the ordinary one. The only relevance in their distinction is to indicate whether or not the problem is a single or multi-variable one, right?

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# Ordinary vs. partial derivatives

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