If $\circ$ represents the Hadamard product, and $^*$ the conjugate-transpose operation. Given
$$f_{(\mathbf{x})} =(\mathbf{x} \circ \mathbf{x})^*H(\mathbf{x} \circ \mathbf{x}) - (\mathbf{x} \circ \mathbf{x})^*\mathbf{y}$$ $H$ is Hermitian, $\mathbf{x}$ and $\mathbf{y}$ are complex-valued.
How can we obtain the derivative of $f_{(\mathbf{x})}$ with respect to $\mathbf{x}$?
Thanks in advance.