Why does -u^-1(∂_μu)u^-1 = ∂_μ(u^-1) for gauge group elements?

[Kontilera]

Hello there!
I'm trying to read a set of notes on the standard model and the author states the following equality without any explanation:
$$-u^{-1}(\partial_\mu u)u^{-1} = \partial_\mu(u^{-1}),$$
u is here a NxN representation of some continuous gauge group and is a function over spacetime.
Does this equality hold and in that case why?

Thanks!
// Kontilera

 

[Kontilera]

Solved it!
Thanks!