Deriving ##\nabla_a w_b## Using Leibniz Rule & Definition

[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 !

 

[binbagsss]

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