]> $$\begin{array}{rcl}Ai\prime \left(0\right)& =& -\frac{1}{3^{\frac{1}{3}}\Gamma \left(\frac{1}{3}\right)}\\ Ai\prime \left(z\right)& =& \frac{z}{\pi \sqrt{3}}{K}_{\pm \frac{2}{3}}\left(\zeta \right)& ;& \zeta =\frac{2}{3}{z}^{\frac{2}{3}}\\ Ai\prime \left(-z\right)& =& \frac{z}{3}\left(J_{\frac{2}{3}}\left(\zeta \right)-J_{-\frac{2}{3}}\left(\zeta \right)\right)\end{array}$$