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