derivative of quadratic function without transposes I'm trying to solve an equation of the following form:
$$ \frac{\partial}{\partial X} A'XA'X $$
where $X$ and $A$ are both equal-length column vectors (and so that $A'XA'A$ is scalar). From looking online I've seen derivatives of forms like $X'X$, but I'm unsure how it would work here when neither $X$ is transposed. My guess was
$$ 2A'AX $$
just to ensure that the derivative is also scalar, but I don't have confidence in that.

Define a scalar
$$b=A'X$$
Then you get
$$\frac{\partial }{\partial X}b^2=2b\frac{\partial b}{\partial X}$$
With
$$\frac{\partial b}{\partial X}=A$$
you finally get for the derivative
$$2bA=2(A'X)A$$
