I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that
$\dfrac{dx}{dt}$ is not a fraction it only behaves like a fraction!
(it means $\dfrac{dx}{dt}$ is just a notation to represent that big limit!) and he made a statement that
$dx$ or $dt$ does not have any meaning it is just $\dfrac{d}{dt}(x)$ which has meaning but we treat it as $\dfrac{dx}{dt}$.
but at same time my physics sir, to derive velocity he stated
let the particle be at position $x$ at time $t$ and after an infinitesimal change in position and time it reaches $x+dx$ at time $t+dt$. Now velocity is $\dfrac{displacement}{time}$ , so we will get $v=\dfrac{dx}{dt}$
and this expression purely tells that $\dfrac{dx}{dt}$ is a fraction!
Now i don't know who is correct, so please help!
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