$A(t)= \pmatrix{\alpha(t)^2&2\alpha(t)\beta(t)&...&...\\...&\alpha(t)\bar{\alpha}(t)-\beta(t)\bar{\beta}(t)&...&...\\...&...&2\alpha\bar{\alpha}\beta-\beta^2\bar{\beta}&...}$
I am meant to find $A'(t)$ and thus $A'(0)$. The $...$ are just other terms that I did not write out as its not necessary for my question below (some are quite long!).
So obviously for $A'(t)$, terms like $\alpha(t)^2$ become $2\alpha'(t)$, and I used the product rule to differentiate $2\alpha(t)\beta(t)$ and it becomes $2(\alpha'(t)\beta(t)+\alpha(t)\beta'(t))$ etc..
The problem is when I come across $2\alpha\bar{\alpha}\beta-\beta^2\bar{\beta}$, how would I find $A'(t)$? Since there are 3 terms $\alpha$, $\bar{\alpha}$ and $\beta$.