Given vectors $\mathbf{a}$ and $\mathbf{b}$, I am looking for the derivative of the following scalar function

$$y(\mathbf{X}) = \mathbf{a}^T\mathbf{X}^2\mathbf{b}$$

with respect to matrix $\mathbf{X}$. I couldn't find a direct answer from [Wikipedia](https://en.wikipedia.org/wiki/Matrix_calculus#Scalar-by-matrix_identities).