Commutator algebra in general relativity

Question

How can we verify the result that

$$[f\textbf{X},\textbf{Y}]= f[\textbf{X}, \textbf{Y}] - \textbf{Y} \left( f \right) \bf{X}$$

Where:

f- Some function

$\textbf{X}, \textbf{Y}$ - Some vector fields