# Absolute derivative

1. Apr 27, 2012

### rbwang1225

1. The problem statement, all variables and given/known data
Please show that the absolute derivative is a vector field along $\gamma$, i.e., $(\frac{d\lambda ^{a'}}{du}+\Gamma^{a'}_{b'c'}\lambda^{b'}\frac{dx^{c'}}{du})=X^{a'}_d(\frac{d\lambda ^{d}}{du}+\Gamma^{d}_{ef}\lambda^{e}\frac{dx^{f}}{du})$
3. The attempt at a solution
I don't know how to reduce the following eq. $(\frac{d\lambda ^{a'}}{du}+\Gamma^{a'}_{b'c'}\lambda^{b'}\frac{dx^{c'}}{du}) = X^{a'}_{bc}\lambda ^b\dot x ^c+X^{a'}_b\dot\lambda ^b-\Gamma ^d_{ef}X^{a'}_d\lambda^eX^{d'}_cX^{e'}_g X^f_{d'e'}\dot x^gx^c+\dot x^f\Gamma^d_{ef}X^{a'}_d \lambda^e$
Any comment would be appreciated.