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。
\[ \begin{equation}\begin{split}【1/1】求函数{10}^{lg(sin(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {10}^{lg(sin(x))}\right)}{dx}\\=&({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))\\=&\frac{{10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos(x)}{ln{10}sin(x)} + \frac{{10}^{lg(sin(x))}*0cos(x)}{(10)ln{10}sin(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)}{ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)}{ln{10}}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}*2ln(10)*0cos^{2}(x)}{(10)ln^{2}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2*0cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2cos(x)cos^{2}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2cos(x)sin(x)}{ln^{2}{10}sin^{2}(x)} - \frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}*0cos^{2}(x)}{(10)ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-0cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-2cos(x)cos^{2}(x)}{ln{10}sin^{3}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-2cos(x)sin(x)}{ln{10}sin^{2}(x)} - \frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)}{ln{10}} - \frac{{10}^{lg(sin(x))}*0}{(10)ln{10}} - \frac{{10}^{lg(sin(x))}ln(10)*-0}{ln^{2}{10}}\\=&\frac{{10}^{lg(sin(x))}ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}*3ln^{2}(10)*0cos^{3}(x)}{(10)ln^{3}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3*0cos^{3}(x)}{ln^{4}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3cos(x)cos^{3}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3cos^{2}(x)sin(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}*2ln(10)*0cos^{3}(x)}{(10)ln^{2}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-2*0cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-3cos(x)cos^{3}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-3cos^{2}(x)sin(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}*0cos^{3}(x)}{(10)ln{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-0cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-3cos(x)cos^{3}(x)}{ln{10}sin^{4}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-3cos^{2}(x)sin(x)}{ln{10}sin^{3}(x)} - \frac{3({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}*2ln(10)*0cos(x)}{(10)ln^{2}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-2*0cos(x)}{ln^{3}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-cos(x)cos(x)}{ln^{2}{10}sin^{2}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-sin(x)}{ln^{2}{10}sin(x)} + \frac{2({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos(x)}{ln{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}*0cos(x)}{(10)ln{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{10}^{lg(sin(x))}ln^{4}(10)cos^{4}(x)}{ln^{4}{10}sin^{4}(x)} - \frac{6 * {10}^{lg(sin(x))}ln^{3}(10)cos^{4}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{11 * {10}^{lg(sin(x))}ln^{2}(10)cos^{4}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{6 * {10}^{lg(sin(x))}ln^{3}(10)cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} - \frac{6 * {10}^{lg(sin(x))}ln(10)cos^{4}(x)}{ln{10}sin^{4}(x)} + \frac{14 * {10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{8 * {10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} + \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)}{ln^{2}{10}} - \frac{2 * {10}^{lg(sin(x))}ln(10)}{ln{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{10}^{lg(sin(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {10}^{lg(sin(x))}\right)}{dx}\\=&({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))\\=&\frac{{10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos(x)}{ln{10}sin(x)} + \frac{{10}^{lg(sin(x))}*0cos(x)}{(10)ln{10}sin(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln(10)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)}{ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)}{ln{10}}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}*2ln(10)*0cos^{2}(x)}{(10)ln^{2}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2*0cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2cos(x)cos^{2}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{2}(10)*-2cos(x)sin(x)}{ln^{2}{10}sin^{2}(x)} - \frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}*0cos^{2}(x)}{(10)ln{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-0cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-2cos(x)cos^{2}(x)}{ln{10}sin^{3}(x)} - \frac{{10}^{lg(sin(x))}ln(10)*-2cos(x)sin(x)}{ln{10}sin^{2}(x)} - \frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)}{ln{10}} - \frac{{10}^{lg(sin(x))}*0}{(10)ln{10}} - \frac{{10}^{lg(sin(x))}ln(10)*-0}{ln^{2}{10}}\\=&\frac{{10}^{lg(sin(x))}ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{{10}^{lg(sin(x))}ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)cos(x)}{ln{10}sin(x)}\right)}{dx}\\=&\frac{({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{3}(10)cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}*3ln^{2}(10)*0cos^{3}(x)}{(10)ln^{3}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3*0cos^{3}(x)}{ln^{4}{10}sin^{3}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3cos(x)cos^{3}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{{10}^{lg(sin(x))}ln^{3}(10)*-3cos^{2}(x)sin(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}*2ln(10)*0cos^{3}(x)}{(10)ln^{2}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-2*0cos^{3}(x)}{ln^{3}{10}sin^{3}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-3cos(x)cos^{3}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-3cos^{2}(x)sin(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos^{3}(x)}{ln{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}*0cos^{3}(x)}{(10)ln{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-0cos^{3}(x)}{ln^{2}{10}sin^{3}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-3cos(x)cos^{3}(x)}{ln{10}sin^{4}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-3cos^{2}(x)sin(x)}{ln{10}sin^{3}(x)} - \frac{3({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln^{2}(10)cos(x)}{ln^{2}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}*2ln(10)*0cos(x)}{(10)ln^{2}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-2*0cos(x)}{ln^{3}{10}sin(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-cos(x)cos(x)}{ln^{2}{10}sin^{2}(x)} - \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)*-sin(x)}{ln^{2}{10}sin(x)} + \frac{2({10}^{lg(sin(x))}((\frac{cos(x)}{ln{10}(sin(x))})ln(10) + \frac{(lg(sin(x)))(0)}{(10)}))ln(10)cos(x)}{ln{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}*0cos(x)}{(10)ln{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-0cos(x)}{ln^{2}{10}sin(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-cos(x)cos(x)}{ln{10}sin^{2}(x)} + \frac{2 * {10}^{lg(sin(x))}ln(10)*-sin(x)}{ln{10}sin(x)}\\=&\frac{{10}^{lg(sin(x))}ln^{4}(10)cos^{4}(x)}{ln^{4}{10}sin^{4}(x)} - \frac{6 * {10}^{lg(sin(x))}ln^{3}(10)cos^{4}(x)}{ln^{3}{10}sin^{4}(x)} + \frac{11 * {10}^{lg(sin(x))}ln^{2}(10)cos^{4}(x)}{ln^{2}{10}sin^{4}(x)} - \frac{6 * {10}^{lg(sin(x))}ln^{3}(10)cos^{2}(x)}{ln^{3}{10}sin^{2}(x)} - \frac{6 * {10}^{lg(sin(x))}ln(10)cos^{4}(x)}{ln{10}sin^{4}(x)} + \frac{14 * {10}^{lg(sin(x))}ln^{2}(10)cos^{2}(x)}{ln^{2}{10}sin^{2}(x)} - \frac{8 * {10}^{lg(sin(x))}ln(10)cos^{2}(x)}{ln{10}sin^{2}(x)} + \frac{3 * {10}^{lg(sin(x))}ln^{2}(10)}{ln^{2}{10}} - \frac{2 * {10}^{lg(sin(x))}ln(10)}{ln{10}}\\ \end{split}\end{equation} \]
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