## derivative of trace of a Matrix

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