1. The problem statement, all variables and given/known data I've just started (self-studying) Neuenschwander's Tensor Calculus for Physics and I got stuck at page 23, where he deals with transformations of displacements. I've made a summary of page 23 in the first part of the attached file. 2. Relevant equations I want to use the coordinates x(x', y', z'), y(x', y', z'), z(x', y', z') and x'(x,y,z), y'(x,y,z), z'(x,y,z) and try to reverse the original transformation from unprimed to primed, see attached file. 3. The attempt at a solution I get a result which seems to say that dx'= 3dx', see attached file. So I don't understand where I'm going wrong. I'd be very grateful if anyone could help.