Drive the inverse position equation . based on the differentiation to the inverse position equation , we get the analytic expression of the inverse jacobian matrix " j - 1 " , the expression is the foundation of the research in many performance indexes 建立了机构的位置反解方程，并利用对反解方程进行求导的方法，得到了机构的逆雅可比矩阵j ~ ( - 1 )的解析表达式，这个表达式是分析机构各种性能指标的基础。
On one hand , numerical derivatives provide proper search directions in optimization , therefore their accuracy is of great importance for fast convergency . on the other hand , derivative evaluation is one of the most time - consuming steps in optimization 当前的高性能数学规划算法大都依赖于导数计算以快速收敛到最优点，所以对求导精度的要求比较高；而导数计算所消耗的时间占优化时间的比例又非常的大。
Some economic characteristic indices , such as the marginal condition for enterprise ' s profit maximization , and substitution property of different comodities etc . under certain market environment , can be analysed by using the said model 按照经济分析的要求，利用数学求导的链式法则，建立了描述热力系统生产特性的热经济学模型，可分析在特定市场环境下企业利润最大化的边际条件、产品替代特性等经济性能指标。
Automatic differentiation ( ad ) , which is well recognized as the most promising differentiation algorithm in pso and has been developed rapidly in recent twenty years , is a technique for augmenting computer programs with derivative computations 在过程系统优化中，一个理想的求导算法应该能够快速求取程序模块的解析导数。近年来发展迅速的自动微分算法比较好地满足了这个条件，并已在优化中得到了广泛的应用。
In the use of the recurrence definition and the matrix presentation of nurbs curve , the algorithm of curve is outlined from the correspondent algorithm of b - spline , concerning on the evaluating , derivative , integral , knots inserting and degree elevating 利用nurbs曲线基函数的定义和nurbs曲线的矩阵表示，从b样条的相关算法出发，可解决nurbs曲线的求值、求导、求积算法和nurbs曲线的节点、升阶算法等问题。
The errors in calculating derivatives for the gll collocation points are evaluated , which can be alleviated from o ( ( n4 ) to o ( ( n2 ) by the double - precision method proposed in the present paper , where ( denotes the machine precision and n the order of the interpolation polynomials in the elements 文中对gll配置点下的求导误差进行了分析，提出的双精度方法可以将求导误差从o ( ( n4 )减小到o ( ( n2 ) ，其中(为机器精度， n为单元内插值多项式阶数。
Arranging velocity and acceleration sensors simultaneously in the same station , in the identical round of holes , under the condition of the same sample frequency , the differential values of velocities should tally with the actual measurement values of acceleration or be in the range of allowable error 摘要在同一测点同时布置了速度和加速度传感器，在同一炮次中，在同样的采样频率情况下，速度值求导应该与实测加速度相吻合或在误差允许范围内。
Sad is able to differentiate models in form of subroutines , fully exploit the sparsity of the models and need few additional operations . it is concluded that sad is very suitable for the process models that have relatively simple computational structure and consist mainly of polynomials 符号自动微分具有可对子程序形式的函数求导、可以充分利用模型的稀疏性、无需辅助操作的优点，非常适合针对结构相对简单、计算式以多项式为主的过程系统模型求导。
In digital relay , the percentage of noise will increase rapidly with the increase of sampling rate when derivation calculus is substituted by sampled difference term . to solve this problem , a new method using fragment function integrated with the least square algorithm is proposed in this paper . the influence of white noise is greatly reduced and the accuracy of the dead angle calculation is nicely improved after adopting the new method 在数字式保护中，如果用差分代替求导将导致噪声的百分比误差随着采样频率的提高而剧增，本文对此进行了分析并提出了用分段样条函数最小二乘法来计算电流波形的导数值，以便在提高采样率的同时降低噪声误差的影响，并将其应用于基于32位浮点dsp的新型变压器保护装置。
Because limited by the sampling channel of transient electromagnetic measuring depth fieldwork curve ( generally 20 ~ 40 channels ) , the smoothing degree of fieldwork curve is not very good , it make against the differential imaging treatment . in order to hold the continuous change characters of the curve and seek the voltage exactly , we use the thrice spline insert number function to reconstruct the fieldwork data ; 4 ) t ； 3 .由于受瞬变电磁测深实测曲线取样道的限制(一般为20 ~ 40道) ，实测曲线光滑程度较差，不利于微分成像处理，为了更好的把握曲线连续变化的特征及准确求导，采用了三次样条插值对实测数据进行重构;续
