I came across the following equality
$[\text{grad} f, X] = \nabla_{\text{grad} f} X + \nabla_X \text{grad} f$
Is this true, and how can I prove this (without coordinates)?
I came across the following equality
$[\text{grad} f, X] = \nabla_{\text{grad} f} X + \nabla_X \text{grad} f$
Is this true, and how can I prove this (without coordinates)?