Lame matrix calculus question: Suppose you have that $y$ is an $n \times 1$ vector function of $t$ and $G$ is an $n \times n$ symmetric matrix function of $t$. Is it ok to write
$\frac{d}{dt}(y^T G y) = 2 \frac{d(y^T)}{dt} G y + y^T \frac{dG}{dt}y$,
where superscript $T$ denotes the transpose?