Common Borel radius of an algebroid function and its derivative

In this article, by comparing the characteristic functions, we prove that for any $\nu$-valued algebroid function $w(z)$ defined in the unit disk with ${\mathrm{lim\hspace{0.17em}sup}}_{r\to 1-}T(r,w)\mathrm{/}\log \frac{1}{1-r}=\mathrm{\infty }$ and the hyper order ${\rho }_2(w)=0$, the distribution of the Borel radius of $w(z)$ and $w^{\mathrm{\prime }}(z)$ is the same. This is the extension of G. Valiron’s conjecture for the meromorphic functions defined in $\widehat{\mathbb{C}}$.