I've been working on my dynamics homework when I've run into confusion with derivatives and could use some help regarding that. The question is as follows: When varying a functional with respect to a variable, do we consider different derivatives of functions to be independent? For instance, what...

I often see in physics that, we say that we can multiply infinitesimals to use chain rule. For example, $$ \frac{dv}{dt} = \frac{dv}{dx} * v(t)$$ But, what bothers me about this is that it raises some serious existence questions force me, when we say that we take derivative of $v$ velocity with r...

The fastest camera available so far is capturing 10 millions images per second. https://www.shimadzu.fr/hyper-vision-hpv-x2 In the scenario of the currently known physics, but in the hypothesis where technology would allow to have a video camera so fast that it would be able to store images at ro...