Question

What is the differences between these two equations?

1- $\upsilon$_x = $dx/dt$

and

2- $\upsilon$_x = $∂x/∂t$

In my book there are equations use d and others use ∂.

Please tell me the differences.

Answer 1

When they write $d/dt$ (full derivative) they assume that the function $x$ depends only on one variable, $t$. Thus, it will be $x(t)$.

When they write $\partial/\partial t$ (partial derivative), they assume that the function $x$ depends on several variables, including $t$ and the derivative is taking only with respect to $t$, while treating all other variables as constants. So it might be something like that $x(t,y,z)$. The number and the nature of these variables, of course, depend on the context.