Abstract: A novel algorithm to calculate first and second derivatives in lens optimization design is described.Based on the differential law of complex function,the first and second analytical derivatives of ray coordinates in the image plane with respect to parameters such as radius,thickness etc.can be obtained from only one raytracing.On the basis of this,the first and second derivatives of the merit function with respect to variables can be easily obtained.The relevant deduction process and examples of computation are also given.The results of practical computations show that it takes much less time (especially for the second derivatives) to obtain the derivatives by the analytical method than by the difference method.