As far as I know, the $n$ coordinates $(x\_1, x\_2, ..., x\_n)$ chosen to describe an $n-$manifold have to be mutually independent $\to$ the mutual derivatives must equal $0$ (for example, $\frac{dx\_1}{dx\_2} = 0$).

Anyway, it seems to me that in Minkowski spacetime (coordinates: $x\_1, x\_2, x\_3, ct$), there is indeed a dependence between any one of the "spatial" coordinate and the "temporal one" (I simply note that for example, $\frac{dx\_1}{dt}$ is the "classical" velocity in $x-$direction, which is clearly not $0$ in general).

So why can this set of coordinates be used to describe a manifold?