Based on the numerical differential theory, it is available to calculate the approximate first derivative of the target-node by using numerical differentiation formulas when the discrete sampling points of the unknown target function on specified interval are given. But for the target-nodes close to the boundary, it may be unable to use the center differentiation formulas involving multiple nodes because of the lack of sampling points on one side of the target-node. Besides, an accelerating change of the first derivative of the target-node may occur in some target functions. However, the use of forward/backward differentiation formulas simply takes the nodes on one side of the target-node into consideration, which probably makes the formulas difficult to adapt to such a change, and thus leads to less accuracy in estimating the first derivative of the target-node. Actually, for the target-nodes close to the right boundary, it is available to move the backward differentiation formulas one node ahead to calculate the first derivatives. Therefore, one-node-ahead numerical differentiation formulas are proposed and investigated. Experimental results verify and show that the first derivatives of the target-nodes with high computational precision can be obtained by using the one-node-ahead numerical differentiation formulas.