I want to take the derivative of $\frac{\beta ^{\mathsf{T}} (A+B)\circ (A+B)}{m}$ with respect to B.
However, I am getting $$\frac{2 (A+B) \beta ^{\mathsf{T}}}{m}$$
Now I believe this is wrong. But I have tried to utilize this rule: please let me know where I have gone wrong and show me how is supposed to be done, not just the answer.
$D[X\circ Y]=X\circ D[Y]+D[X]\circ Y$
Note m is a coefficient, A and B are matrices and beta is a vector.