高阶导数“一题多解”与学生发散思维的培养

On Multi-Solutions of Higher Derivative and Divergent Thinking Fostering in Students

以计算高阶导数"一题多解"为例,利用数学归纳法、有理函数高阶导数公式、莱布尼茨公式、幂级数展开式、分解法分别给出不同的解题方法。旨在帮助学生拓展解题思路、加强对学生发散思维及创新思维的培养、提高学生综合应用数学知识的能力及数学素养。

This paper respectively uses the mathematical induction, rational function higher derivative formula, Leibniz formula, and power series expansion formula and decomposition method to get solutions for higher derivative problems. These multi - solutions could help the students to widen their problem - solving thinking, enhance their divergent thinking and creative thinking, and improve their abilities to apply mathematical knowledge synthetically and mathematical quality.