Question about generalized coordinates.

Hi guys,

I'm currently going through Goldsteins "Classical Mechanics" in preparation for my next semester and i have a question regarding generalized coordinates.

On page 18 he gives the equation of the velocity in terms of the generalized coordinates:

http://ift.tt/2xXbxJ3 (1)

This is perfectly clear to me, simple chain rule. However two pages later on page 20 he states that the equation

http://ift.tt/2yVh5lq (2)

follows directly from Equ.1 and I just cannot see how, when I try derive (2) with (1) I get weird results.

I'd be grateful if someone explained to me how (2) follows from (1)!

Thank you!