The analytic filtered backprojection algorithms are widely used in the computed tomography field. It is well known that the filtering step is implemented either by a ramp kernel function or by combining the derivative and Hilbert filtering operations. Although the derivative is a local operator, the corresponding discrete kernel function has infinite support. It is practical to compute derivative using some numerical methods, such as forward, backward, central differences and spline fitting. In this paper, we numerically evaluate the performance of different numerical methods for computing derivative by fixing other factors. By quantitatively analyzing the reconstructed image quality, we look into tradeoffs between image quality indexes when each type of derivative is used. Results show that, the central difference approximation derivatives produce the most accurate images with lower noise and spatial resolution, whereas the spline fitting leads to the highest spatial resolution with higher noise.