平面曲线的切割函数的第二参数可导性

Derivability of Tangent and Secant Function on Plane Curve with Second Variable

目的研究平面曲线的切割函数关于第二参数的可导性。方法先构造一组形式计算公式,再使用几何分析法。结果得到了平面曲线的切割函数关于第二参数的一阶导数和二阶导数的表达式,以及它们在间断点处的极限值。结论平面曲线的切割函数关于第二参数是可导的,并且它的一阶导数和二阶导数都连续。

Objective To explore derivability of tangent and secant function on plane curve with the second variable. Methods A group of computation formula were constructed and geometry analysis meth- od was used. Results The first derivative and the second derivative expression of the tangent and secant function about the second parameter were obtained, as well as the limits of the discontinuity points of the tangent and secant function. Conclusion The tangent and secant function is derivable about the second parameter, and its first derivatives and second derivatives are continuous.