关于用Lagrange插值算子的一阶导数逼近函数的一阶导数有许多杰出的工作,但人们对用Lagrange插值算子的二阶导数逼近函数的二阶导数有怎样的敛速估计也十分感兴趣.本文我们对一类Lagrange插值算子除给出用其一阶导数逼近函数一阶导数的误差估计外,还将首次给出其二阶导函数逼近函数二阶导函数的误差估计. There are many outstanding works about the first derivative of the first-order derivative approximation function using the Lagrange interpolation operator, but it is also very interesting to find out how to estimate the second derivative of the second derivative approximation function of the Lagrange interpolation operator In this paper, we give the error estimation of a class of Lagrange interpolation operator for the first time, besides the error estimation of the first derivative of the first order derivative approximation function.