Differentiate a function contains modules of a complex vector

Question

The function $f$ has form: $$f(x)=\log (1+ |z^\intercal x|^2)$$ where $z\in C^n, x\in C^n$ are two complex vectors.

How to differentiate $f$ with respect to $x$: $$\frac{df(x)}{dx}=?$$

Any comment would be highly appreciated