Point Transformations in the Lagrangian

[dynamicskillingme]

Homework Statement

Hi, I'm working on understanding how a time independent point transformation

. effects the Lagrangian and to see how what values are co and contra variant.

Homework Equations

Would these be correct formulations, or have I overlooked something?

The Attempt at a Solution

and

for Q = 0, from

 

[facenian]

The left side seems ok. I don't know where the right side comes from, I mean the second factor of the left side.