求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
本次共计算 1 个题目：每一题对 d 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数include^{\frac{stdio}{h}} 关于 d 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = include^{\frac{istod}{h}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( include^{\frac{istod}{h}}\right)}{dd}\\=&inclue^{\frac{istod}{h}} + \frac{include^{\frac{istod}{h}}isto}{h}\\=&inclue^{\frac{istod}{h}} + \frac{i^{2}nclustode^{\frac{istod}{h}}}{h}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( inclue^{\frac{istod}{h}} + \frac{i^{2}nclustode^{\frac{istod}{h}}}{h}\right)}{dd}\\=&\frac{inclue^{\frac{istod}{h}}isto}{h} + \frac{i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{2}nclustode^{\frac{istod}{h}}isto}{hh}\\=&\frac{2i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}}{h^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}}{h^{2}}\right)}{dd}\\=&\frac{2i^{2}nclustoe^{\frac{istod}{h}}isto}{hh} + \frac{i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}isto}{h^{2}h}\\=&\frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}}{h^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}}{h^{3}}\right)}{dd}\\=&\frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}isto}{h^{2}h} + \frac{i^{4}nclus^{3}t^{3}o^{3}e^{\frac{istod}{h}}}{h^{3}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}isto}{h^{3}h}\\=&\frac{4i^{4}nclus^{3}t^{3}o^{3}e^{\frac{istod}{h}}}{h^{3}} + \frac{i^{5}nclus^{4}t^{4}o^{4}de^{\frac{istod}{h}}}{h^{4}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数include^{\frac{stdio}{h}} 关于 d 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = include^{\frac{istod}{h}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( include^{\frac{istod}{h}}\right)}{dd}\\=&inclue^{\frac{istod}{h}} + \frac{include^{\frac{istod}{h}}isto}{h}\\=&inclue^{\frac{istod}{h}} + \frac{i^{2}nclustode^{\frac{istod}{h}}}{h}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( inclue^{\frac{istod}{h}} + \frac{i^{2}nclustode^{\frac{istod}{h}}}{h}\right)}{dd}\\=&\frac{inclue^{\frac{istod}{h}}isto}{h} + \frac{i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{2}nclustode^{\frac{istod}{h}}isto}{hh}\\=&\frac{2i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}}{h^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2i^{2}nclustoe^{\frac{istod}{h}}}{h} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}}{h^{2}}\right)}{dd}\\=&\frac{2i^{2}nclustoe^{\frac{istod}{h}}isto}{hh} + \frac{i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{3}nclus^{2}t^{2}o^{2}de^{\frac{istod}{h}}isto}{h^{2}h}\\=&\frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}}{h^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}}{h^{2}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}}{h^{3}}\right)}{dd}\\=&\frac{3i^{3}nclus^{2}t^{2}o^{2}e^{\frac{istod}{h}}isto}{h^{2}h} + \frac{i^{4}nclus^{3}t^{3}o^{3}e^{\frac{istod}{h}}}{h^{3}} + \frac{i^{4}nclus^{3}t^{3}o^{3}de^{\frac{istod}{h}}isto}{h^{3}h}\\=&\frac{4i^{4}nclus^{3}t^{3}o^{3}e^{\frac{istod}{h}}}{h^{3}} + \frac{i^{5}nclus^{4}t^{4}o^{4}de^{\frac{istod}{h}}}{h^{4}}\\ \end{split}\end{equation} \]