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As for my knowledge there are 3 different notations for showing derivative for $f:C\to S\left(C,S\subseteq\Bbb R\right)$:

$f'$-Lagrange's way

$\dfrac{df}{dx}$ - Leibniz's way

$\dot{f}$ - Newton's way

my question is:

is there a fundamental difference between the 3 ways? for example i know that Newton's notation is mainly used in physics in respect to time. does it mean that this way gives a different result from the 2 others? or maybe Newton talked about it in a function that is in respect to time the first time and it like this today solely because of historical reasons?

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  • $\begingroup$ The Leibniz notation also alludes to the use of $\text d x$ for a differential, which in some sense could be seen as a deep thing. However this is just a fact about coinciding notation and not a fact about single variable derivatives -- the three things you wrote are equal, and there's not more to it than that. $\endgroup$ – neptun Nov 2 '17 at 10:05
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These 3 different notations are notations of exactly the same thing, the derivative. It is customary in physics and engineering to denote a spatial derivative in Lagrange's way, and a time derivative in Newton's way, but there is nothing deep into it, it is just customary.

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