I'm trying to brush up on my calculus for my job search and I'm really struggling to understand something basic that is frustrating me. The question is given by:
If w $\in \mathbb{R}^d$ and x $\in \mathbb{R}^d$ and $f(w) = sin(x^Tw)$, find $\frac{\partial f(w)}{\partial w}$ and $\frac{\partial^2 f(w)}{\partial w\partial w^T}$
Now I'm pretty sure I can get the first derivative correctly at $x^Tcos(x^Tw)$ but I'm struggling to understand the notation of the second derivative, in particular $\partial w\partial w^T$. Am I correct in saying that this question is asking for the derivative with respect to W of the derivative with respect to $w^T$? But, how does one find this $w^T$ to begin with?