Just a quick question; I have "notation indigestion", i.e., I have been trying

to figure way too many technicalities recently; I would appreciate a quick yes/no:

Say X_p is a V.Field defined at p in a C^k manifold; k>0 . Say (U,Phi) and (U',Phi')

are both charts containing p . Just wondering if the rule for coordinate change

of X from chart-to-chart is; is it given by

d(Phi o Phi'^-1) and d(Phi' o Phi^-1) ?

I mean, I know it involves the chain rule, but I wonder if it is the chain rule

applied to the two formulas above.

Thanks.