Vector-by-Vector derivative Could someone please help me out with this derivative?
$$
\frac{d}{dx}(xx^T)
$$
with both $x$ being vector.
Thanks
EDIT:
I should clarify that the actual state I am taking the derivative is
$$
\frac{d}{dx}(xx^TPb)
$$
where $Pb$ has the dimention of $x$ but is independent of $x$. So the whole state $xx^TPb$ is a vector. 
EDIT2:
Would it become by any chance the following?
$$
\frac{d}{dx}(xx^TPb) = (Pbx^T)^T + x(Pb)^T = 2x(Pb)^T
$$

You can always go back to the basics.  Let $v$ be any vector and $h$ a real number.  Substitute $x \leftarrow x + h v$ to get
$$
(x + hv)(x+hv)^t = (x+hv)(x^t+hv^t) = x x^t + h(xv^t + vx^t) + h^2 vv^t.
$$
The linear term in $h$ is your derivative at $x$ in the direction of $v$, so $xv^t + vx^t$ (which is linear in $v$ as expected).
