Suppose I have some coordinates $q_i$ ($i=1,2,...,n$) and consider an invertible transformation thereof to some other set of coordinates, $x_j = x_j(q_1,...,q_n)$ ($j=1,2,...n$).
My textbook (Shankar's quantum mechanics textbook, in Chapter 2 when discussing changes of coordinates in configuration space in the classical Lagrangian picture -- this is equation 2.7.7, the first equality, for those who have the book) states that $$\frac{dx_i}{dt}=\frac{dq_i}{dt}$$ if we write the right-hand side in terms of the $x_i$. This seems to me to be to be incorrect in general, and I'm hoping someone can confirm.