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。
\[ \begin{equation}\begin{split}【1/1】求函数ln({x}^{cos({x}^{2})}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln({x}^{cos(x^{2})})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln({x}^{cos(x^{2})})\right)}{dx}\\=&\frac{({x}^{cos(x^{2})}((-sin(x^{2})*2x)ln(x) + \frac{(cos(x^{2}))(1)}{(x)}))}{({x}^{cos(x^{2})})}\\=&-2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\right)}{dx}\\=&-2ln(x)sin(x^{2}) - \frac{2xsin(x^{2})}{(x)} - 2xln(x)cos(x^{2})*2x + \frac{-cos(x^{2})}{x^{2}} + \frac{-sin(x^{2})*2x}{x}\\=&-2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\right)}{dx}\\=&\frac{-2sin(x^{2})}{(x)} - 2ln(x)cos(x^{2})*2x - 4cos(x^{2})*2x - 4*2xln(x)cos(x^{2}) - \frac{4x^{2}cos(x^{2})}{(x)} - 4x^{2}ln(x)*-sin(x^{2})*2x - \frac{-2cos(x^{2})}{x^{3}} - \frac{-sin(x^{2})*2x}{x^{2}}\\=& - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\right)}{dx}\\=& - 12ln(x)cos(x^{2}) - \frac{12xcos(x^{2})}{(x)} - 12xln(x)*-sin(x^{2})*2x - 12cos(x^{2}) - 12x*-sin(x^{2})*2x + 8*3x^{2}ln(x)sin(x^{2}) + \frac{8x^{3}sin(x^{2})}{(x)} + 8x^{3}ln(x)cos(x^{2})*2x + \frac{2*-3cos(x^{2})}{x^{4}} + \frac{2*-sin(x^{2})*2x}{x^{3}}\\=& - 12ln(x)cos(x^{2}) - 24cos(x^{2}) + 48x^{2}ln(x)sin(x^{2}) + 32x^{2}sin(x^{2}) + 16x^{4}ln(x)cos(x^{2}) - \frac{6cos(x^{2})}{x^{4}} - \frac{4sin(x^{2})}{x^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数ln({x}^{cos({x}^{2})}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln({x}^{cos(x^{2})})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln({x}^{cos(x^{2})})\right)}{dx}\\=&\frac{({x}^{cos(x^{2})}((-sin(x^{2})*2x)ln(x) + \frac{(cos(x^{2}))(1)}{(x)}))}{({x}^{cos(x^{2})})}\\=&-2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\right)}{dx}\\=&-2ln(x)sin(x^{2}) - \frac{2xsin(x^{2})}{(x)} - 2xln(x)cos(x^{2})*2x + \frac{-cos(x^{2})}{x^{2}} + \frac{-sin(x^{2})*2x}{x}\\=&-2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\right)}{dx}\\=&\frac{-2sin(x^{2})}{(x)} - 2ln(x)cos(x^{2})*2x - 4cos(x^{2})*2x - 4*2xln(x)cos(x^{2}) - \frac{4x^{2}cos(x^{2})}{(x)} - 4x^{2}ln(x)*-sin(x^{2})*2x - \frac{-2cos(x^{2})}{x^{3}} - \frac{-sin(x^{2})*2x}{x^{2}}\\=& - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\right)}{dx}\\=& - 12ln(x)cos(x^{2}) - \frac{12xcos(x^{2})}{(x)} - 12xln(x)*-sin(x^{2})*2x - 12cos(x^{2}) - 12x*-sin(x^{2})*2x + 8*3x^{2}ln(x)sin(x^{2}) + \frac{8x^{3}sin(x^{2})}{(x)} + 8x^{3}ln(x)cos(x^{2})*2x + \frac{2*-3cos(x^{2})}{x^{4}} + \frac{2*-sin(x^{2})*2x}{x^{3}}\\=& - 12ln(x)cos(x^{2}) - 24cos(x^{2}) + 48x^{2}ln(x)sin(x^{2}) + 32x^{2}sin(x^{2}) + 16x^{4}ln(x)cos(x^{2}) - \frac{6cos(x^{2})}{x^{4}} - \frac{4sin(x^{2})}{x^{2}}\\ \end{split}\end{equation} \]
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