# differences in derivative notation

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?

• 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. – neptun Nov 2 '17 at 10:05