I am reading a paper and can't understand the following step.
Let $\Phi_j$ be a complex vector and $W$ a real symmetric, positive definite and block diagonal matrix. Both $\Phi_j$ and $W$ depend on some parameter $p$. Let $(\cdot)^H$ denote the conjugate transpose of a vector and $\overline{(\cdot)}$ the conjugate.
By differentiating the equation $\Phi^H_jW\Phi_j$ w.r.t. $p$ the author derives the following equation:
$$\frac{d}{d p}(\Phi^H_jW\Phi_j) = \Phi^H_jW\frac{d\Phi_j }{d p}+ \overline{\Phi^H_jW\frac{d\Phi_j }{d p}}$$
Is this some sort of chain rule? Am I missing the obvious here? Thanks