Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline.
(I'm sorry for my poor English.)
Consider a new coordinate system xµ' which differs from the original Cartesian coordinate system xµ; the Cartesian coordinates xµ can be written as a function of these new coordinates xµ = xµ (xµ'). Show that the equation of motion can be written in these new xµ' coordinates as ξ²xµ' + Γµ'ν'λ'ξxν'ξxλ' = 0 for some Γµ'ν'λ' which you must compute; Γµ'ν'λ' is known as the Christoffel symbol. These extra Christoffel terms in the equation of motion can be thought of as ”fictitous forces” that arise in an accelerated reference frame.
xµ' = Jac * xµ
The Attempt at a Solution
I've tried to solve this by deriving xµ' with respect to φ using the chain rule, but that did not work. Unfortunately I could not put my work here, but it was just what I said: I've used the chain rule to derive xµ' with respect to φ.