Piecewise functions often appeared in Advanced Mathematics.The derivation for piecewise points is always one of the difficulties in students' learning.We are usually based on the definition of the derivative to judge the differentiability of piecewise points,and students feel very difficult.In this paper,a detailed carding for methods to judge the piecewise function's differentiability at piecewise points is given.Using the derivation formula,the derived function of the piecewise point left and right side for Piecewise functions that satisfy certain conditions can be obtained respectively.Then we get left derivative and right derivative with substituting piecewise point,and the piecewise function's differentiability of piecewise points can be educed.It can make the calculation process greatly simplified which is more easy.for students.%分段函数在《高等数学》中经常出现,其分段点处的求导问题一向是学生学习的一大难点。通常我们是依据导数定义来判断分段点处的可导性,学生实际用起来感觉很吃力。对分段函数在分段点处可导性的判别方法做了详细梳理,对满足一定条件的分段函数,利用求导公式分别求出分段点左、右两侧的导函数,再将分段点代入作为分段点处的左、右导数,并以此得出分段函数在分段点处的可导性,这样做可使计算过程大大简化,更易于学生接受。
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