Understanding a Lagrangian partial derivative derivation involving a coordinate change

Question

In the context of a coordinate change from $q \rightarrow q'$ and $\dot{q} \rightarrow \dot{q'}$

On pg. 139 of No-Nonsense Classical Mechanics the author asserts:

Question: What justifies the very last step, namely that

$$ \frac{\partial}{\partial \dot{q}'} \left(\frac{\partial q}{\partial q'} \dot{q}' + \frac{\partial q}{\partial t} \right) = \frac{\partial q}{\partial q'} $$

?