# Lie Derivative (directional derivative proof)

• Nov 26th 2012, 11:14 AM
supaman5
Lie Derivative (directional derivative proof)
Hi,

http://www.staff.science.uu.nl/~ban0...tes/lieder.pdf

I just need help understanding one line of the proof in this pdf. It's top of page 5, how does the chain rule lead us to the second line from the bottom (the line where the t=0 moves to the end) of the proof?

Why is the line not df/dp dp/dt? I thought that's what the chain rule was...
• Nov 27th 2012, 05:32 AM
xxp9
Re: Lie Derivative (directional derivative proof)
dmf is kind of df/dp
and d\phai /dt is kind of dp/dt
so you're right.
• Nov 28th 2012, 05:31 AM
supaman5
Re: Lie Derivative (directional derivative proof)
Thanks xxp9, but if dmf means df/dm, how does the first denominator, dm, cancel with the second numerator, dphai?
• Nov 28th 2012, 06:42 AM
xxp9
Re: Lie Derivative (directional derivative proof)
The chain rule doesn't need anything to be cancelled. The chain rule just states: The induced linear map of a composition is the composition of the induced linear maps.