I"m looking at "Principles of Dynamics: Second Edition" by Donald T Greenwood. I'm trying to figure out how he obtains Eq. (6-64)
$$\frac{\partial\dot x_j}{\partial\dot q_i} = \frac{\partial x_j}{\partial q_i}\tag{6-64}$$
from Eq (6-54)
$$\dot x_j = \sum_{i=1}^n \frac{\partial x_j}{\partial q_i}\dot q_i + \frac{\partial x_j}{\partial t}.\tag{6-54}$$
where the transformation equations from a set of $3N$ Cartesian coordinates to a set of $n$ generalized coordinates are of the form given by Eq (6-1)
$$x_1=f_1(q_1,q_2,...,q_n,t)$$ $$x_2=f_2(q_1,q_2,...,q_n,t)$$ $$\vdots$$ $$x_{3N}=f_{3N}(q_1,q_2,...,q_n,t).\tag{6-1}$$
When I differentiate Eq (6-54) with respect to $q_i$ I get second derivatives and I have no idea how the term $\frac{\partial^2 x_j}{\partial t\partial \dot q_i}$ is dealt with. Any insight appreciated.