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Is it safe to ignore derivatives of velocity w.r.t. position and vice versa?
In a certain textbook a function is given as:
$$f=f(x(t))$$
And then this is differentiated w.r.t. $t$ to get:
$$f_t=\dot{x}f_x$$
(Where the notation $f_u=df/du$, $f_{uu}=d^2f/du^2$, etc.)
This ...
