Here is a snip of the fundamental relation:
This is from the book "Intro to Smooth Manifolds" and in this section it is simplified down to F as a map between just the real spaces R^n -> R^m (as shown above).
I understand the meaning of this relation, as the following: The rightside is the...
Summary: I'm stuck on this simple excersize, to show that in this coord transform, despite x = x', d/dx != d/dx'
From "Intro to Smooth Manifolds" (this is a calculus excersize), The Problem I have is with showing d/dx != d/dx'
When I write out the Jacobian matrix, I get exactly d/dx = d/dx'...