This paper is a continuation of the research dealing with the connection between circle packing and the Riemann mapping theorem. In this article the authors investigate how well the derivatives of the Riemann mapping can be approximated by the derivatives (with respect to \(z)\) of the discrete mappings \(\{f_ \varepsilon(z)\}\). We quote the main result of the paper: Theorem 2.4: Let \(f_ \varepsilon(z)\) be the circle packing approximation to the Riemann mapping function \(f:\Omega\to\mathbb{D}\). Let \(f_ \varepsilon',f_ \varepsilon''\) be the first and second derivatives of \(f_ \varepsilon(z)\) (see for the precise definition, Lemma 2.1 in the paper). Let \(K\Subset\Omega\). There exists a constant \(C_ k\) s.t. for all \(z\in K:| f_ \varepsilon(z)-f(z)|\leq C_ k\varepsilon^{0.1428}\), \(| f_ \varepsilon^{(1)}(z)- f'(z)|\leq C_ k\) \(\varepsilon^{0.1428/2}\), \(| f_ \varepsilon^{(2)}(z)-f''(z)|\leq C_ k\varepsilon^{0.1428/4}\).