todo

${\bf x}(t)=\sum_{i=1}^nx^i(t){\bf e}_i(t)$

$\dfrac{\partial }{\partial t}{\bf x}(t)=\sum_{i=1}^n\left(\left(\dfrac{\partial }{\partial t}x^i(t)\right){\bf e}_i(t)+x^i(t)\dfrac{\partial }{\partial t}{\bf e}_i(t)\right)$

https://en.wikipedia.org/wiki/Fictitious_force

Wikipedia: https://en.wikipedia.org/wiki/Fictitious_force

Fréchet derivative