A quick question:
F(x) = F_0 + \sum_i x_i F_i where F_i are symmetric matrices and x is a vector

is the following true ??
\frac{d}{dx}trace(F(x)) = trace(\frac{d}{dx}F(x))

and is then this correct (I'm not sure)??
\frac{d}{dx_i} -trace(F(x)^{-1}F_i) = trace(F(x)^{-1}F_iF(x)^{-1}F_i)

thanks