Gradient of quadratic vector function [duplicate]
Solution 1:
The top row of your derivative is incorrect. For example, the coefficient of the $x_2$ term for example will be $(A_{12} + A_{21})$ not just $A_{12}$. This is because the expression $x^TAx$ contains $A_{12}x_1x_2 + A_{21}x_2x_1$. You considered the first term but neglected the second.