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 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数({x}^{3} + 3{x}^{2} + x - 1)lg(cos(e^{arcsin(t)})) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{3}lg(cos(e^{arcsin(t)})) + 3x^{2}lg(cos(e^{arcsin(t)})) + xlg(cos(e^{arcsin(t)})) - lg(cos(e^{arcsin(t)}))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{3}lg(cos(e^{arcsin(t)})) + 3x^{2}lg(cos(e^{arcsin(t)})) + xlg(cos(e^{arcsin(t)})) - lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&3x^{2}lg(cos(e^{arcsin(t)})) + \frac{x^{3}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + 3*2xlg(cos(e^{arcsin(t)})) + \frac{3x^{2}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + lg(cos(e^{arcsin(t)})) + \frac{x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} - \frac{-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&3x^{2}lg(cos(e^{arcsin(t)})) + 6xlg(cos(e^{arcsin(t)})) + lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 3x^{2}lg(cos(e^{arcsin(t)})) + 6xlg(cos(e^{arcsin(t)})) + lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&3*2xlg(cos(e^{arcsin(t)})) + \frac{3x^{2}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + 6lg(cos(e^{arcsin(t)})) + \frac{6x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + \frac{-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&6xlg(cos(e^{arcsin(t)})) + 6lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 6xlg(cos(e^{arcsin(t)})) + 6lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&6lg(cos(e^{arcsin(t)})) + \frac{6x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + \frac{6*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&6lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 6lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&\frac{6*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&0\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数({x}^{3} + 3{x}^{2} + x - 1)lg(cos(e^{arcsin(t)})) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{3}lg(cos(e^{arcsin(t)})) + 3x^{2}lg(cos(e^{arcsin(t)})) + xlg(cos(e^{arcsin(t)})) - lg(cos(e^{arcsin(t)}))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{3}lg(cos(e^{arcsin(t)})) + 3x^{2}lg(cos(e^{arcsin(t)})) + xlg(cos(e^{arcsin(t)})) - lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&3x^{2}lg(cos(e^{arcsin(t)})) + \frac{x^{3}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + 3*2xlg(cos(e^{arcsin(t)})) + \frac{3x^{2}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + lg(cos(e^{arcsin(t)})) + \frac{x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} - \frac{-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&3x^{2}lg(cos(e^{arcsin(t)})) + 6xlg(cos(e^{arcsin(t)})) + lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 3x^{2}lg(cos(e^{arcsin(t)})) + 6xlg(cos(e^{arcsin(t)})) + lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&3*2xlg(cos(e^{arcsin(t)})) + \frac{3x^{2}*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + 6lg(cos(e^{arcsin(t)})) + \frac{6x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + \frac{-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&6xlg(cos(e^{arcsin(t)})) + 6lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 6xlg(cos(e^{arcsin(t)})) + 6lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&6lg(cos(e^{arcsin(t)})) + \frac{6x*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))} + \frac{6*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&6lg(cos(e^{arcsin(t)}))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 6lg(cos(e^{arcsin(t)}))\right)}{dx}\\=&\frac{6*-sin(e^{arcsin(t)})e^{arcsin(t)}(\frac{(0)}{((1 - (t)^{2})^{\frac{1}{2}})})}{ln{10}(cos(e^{arcsin(t)}))}\\=&0\\ \end{split}\end{equation} \]