# Corollary of Leibniz rule for Lie bracket

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This is an identity that uses the Leibniz rule to measure the failure of the Lie bracket operation from being $C^\infty$-linear.
Let $X,Y$ be smooth vector fields on a differential manifold $M$ and $f$ be in $C^\infty(M)$. We then have:
$f[X,Y] = [fX,Y] + (Yf)X$