# Deriving covariant differention formula on covectors from the formula on vectors.

1. Oct 9, 2014

### binbagsss

For a vector : $\nabla_a V^b=\partial _a V^b+T^b_{ac}V^c$

I am trying to derive for a covector: $\nabla_a w_b=\partial _a w_b+T^c_{ab}w_c$

I am told to use the Leibniz Rule and the definition that for a scalar $f$ : $\nabla_a f =\partial_a f$ to do so

My thoughts:

Define $w_b$ through the $\nabla$ function: $w_b$= $\nabla _b f$

And I'm not sure what my next move should be.

Many Thanks for any help in advance !

2. Oct 9, 2014

### binbagsss

Is it not possible to edit threads anymore?
Second eq should be a neg sign before T .. !