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。
\[ \begin{equation}\begin{split}【1/1】求函数({x}^{2} + \frac{1}{x} - \frac{36{x}^{1}}{3})sin({x}^{3}) - tan({x}^{2} + 1) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\right)}{dx}\\=&2xsin(x^{3}) + x^{2}cos(x^{3})*3x^{2} + \frac{-sin(x^{3})}{x^{2}} + \frac{cos(x^{3})*3x^{2}}{x} - 12sin(x^{3}) - 12xcos(x^{3})*3x^{2} - sec^{2}(x^{2} + 1)(2x + 0)\\=&2xsin(x^{3}) + 3x^{4}cos(x^{3}) - \frac{sin(x^{3})}{x^{2}} + 3xcos(x^{3}) - 12sin(x^{3}) - 36x^{3}cos(x^{3}) - 2xsec^{2}(x^{2} + 1)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2xsin(x^{3}) + 3x^{4}cos(x^{3}) - \frac{sin(x^{3})}{x^{2}} + 3xcos(x^{3}) - 12sin(x^{3}) - 36x^{3}cos(x^{3}) - 2xsec^{2}(x^{2} + 1)\right)}{dx}\\=&2sin(x^{3}) + 2xcos(x^{3})*3x^{2} + 3*4x^{3}cos(x^{3}) + 3x^{4}*-sin(x^{3})*3x^{2} - \frac{-2sin(x^{3})}{x^{3}} - \frac{cos(x^{3})*3x^{2}}{x^{2}} + 3cos(x^{3}) + 3x*-sin(x^{3})*3x^{2} - 12cos(x^{3})*3x^{2} - 36*3x^{2}cos(x^{3}) - 36x^{3}*-sin(x^{3})*3x^{2} - 2sec^{2}(x^{2} + 1) - 2x*2sec^{2}(x^{2} + 1)tan(x^{2} + 1)(2x + 0)\\=&2sin(x^{3}) + 18x^{3}cos(x^{3}) - 9x^{6}sin(x^{3}) + \frac{2sin(x^{3})}{x^{3}} - 9x^{3}sin(x^{3}) - 144x^{2}cos(x^{3}) + 108x^{5}sin(x^{3}) - 2sec^{2}(x^{2} + 1) - 8x^{2}tan(x^{2} + 1)sec^{2}(x^{2} + 1)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2sin(x^{3}) + 18x^{3}cos(x^{3}) - 9x^{6}sin(x^{3}) + \frac{2sin(x^{3})}{x^{3}} - 9x^{3}sin(x^{3}) - 144x^{2}cos(x^{3}) + 108x^{5}sin(x^{3}) - 2sec^{2}(x^{2} + 1) - 8x^{2}tan(x^{2} + 1)sec^{2}(x^{2} + 1)\right)}{dx}\\=&2cos(x^{3})*3x^{2} + 18*3x^{2}cos(x^{3}) + 18x^{3}*-sin(x^{3})*3x^{2} - 9*6x^{5}sin(x^{3}) - 9x^{6}cos(x^{3})*3x^{2} + \frac{2*-3sin(x^{3})}{x^{4}} + \frac{2cos(x^{3})*3x^{2}}{x^{3}} - 9*3x^{2}sin(x^{3}) - 9x^{3}cos(x^{3})*3x^{2} - 144*2xcos(x^{3}) - 144x^{2}*-sin(x^{3})*3x^{2} + 108*5x^{4}sin(x^{3}) + 108x^{5}cos(x^{3})*3x^{2} - 2*2sec^{2}(x^{2} + 1)tan(x^{2} + 1)(2x + 0) - 8*2xtan(x^{2} + 1)sec^{2}(x^{2} + 1) - 8x^{2}sec^{2}(x^{2} + 1)(2x + 0)sec^{2}(x^{2} + 1) - 8x^{2}tan(x^{2} + 1)*2sec^{2}(x^{2} + 1)tan(x^{2} + 1)(2x + 0)\\=&60x^{2}cos(x^{3}) - 108x^{5}sin(x^{3}) - 27x^{8}cos(x^{3}) - \frac{6sin(x^{3})}{x^{4}} + \frac{6cos(x^{3})}{x} - 27x^{2}sin(x^{3}) - 27x^{5}cos(x^{3}) - 288xcos(x^{3}) + 972x^{4}sin(x^{3}) + 324x^{7}cos(x^{3}) - 24xtan(x^{2} + 1)sec^{2}(x^{2} + 1) - 16x^{3}sec^{4}(x^{2} + 1) - 32x^{3}tan^{2}(x^{2} + 1)sec^{2}(x^{2} + 1)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 60x^{2}cos(x^{3}) - 108x^{5}sin(x^{3}) - 27x^{8}cos(x^{3}) - \frac{6sin(x^{3})}{x^{4}} + \frac{6cos(x^{3})}{x} - 27x^{2}sin(x^{3}) - 27x^{5}cos(x^{3}) - 288xcos(x^{3}) + 972x^{4}sin(x^{3}) + 324x^{7}cos(x^{3}) - 24xtan(x^{2} + 1)sec^{2}(x^{2} + 1) - 16x^{3}sec^{4}(x^{2} + 1) - 32x^{3}tan^{2}(x^{2} + 1)sec^{2}(x^{2} + 1)\right)}{dx}\\=&60*2xcos(x^{3}) + 60x^{2}*-sin(x^{3})*3x^{2} - 108*5x^{4}sin(x^{3}) - 108x^{5}cos(x^{3})*3x^{2} - 27*8x^{7}cos(x^{3}) - 27x^{8}*-sin(x^{3})*3x^{2} - \frac{6*-4sin(x^{3})}{x^{5}} - \frac{6cos(x^{3})*3x^{2}}{x^{4}} + \frac{6*-cos(x^{3})}{x^{2}} + \frac{6*-sin(x^{3})*3x^{2}}{x} - 27*2xsin(x^{3}) - 27x^{2}cos(x^{3})*3x^{2} - 27*5x^{4}cos(x^{3}) - 27x^{5}*-sin(x^{3})*3x^{2} - 288cos(x^{3}) - 288x*-sin(x^{3})*3x^{2} + 972*4x^{3}sin(x^{3}) + 972x^{4}cos(x^{3})*3x^{2} + 324*7x^{6}cos(x^{3}) + 324x^{7}*-sin(x^{3})*3x^{2} - 24tan(x^{2} + 1)sec^{2}(x^{2} + 1) - 24xsec^{2}(x^{2} + 1)(2x + 0)sec^{2}(x^{2} + 1) - 24xtan(x^{2} + 1)*2sec^{2}(x^{2} + 1)tan(x^{2} + 1)(2x + 0) - 16*3x^{2}sec^{4}(x^{2} + 1) - 16x^{3}*4sec^{4}(x^{2} + 1)tan(x^{2} + 1)(2x + 0) - 32*3x^{2}tan^{2}(x^{2} + 1)sec^{2}(x^{2} + 1) - 32x^{3}*2tan(x^{2} + 1)sec^{2}(x^{2} + 1)(2x + 0)sec^{2}(x^{2} + 1) - 32x^{3}tan^{2}(x^{2} + 1)*2sec^{2}(x^{2} + 1)tan(x^{2} + 1)(2x + 0)\\=&120xcos(x^{3}) - 720x^{4}sin(x^{3}) - 540x^{7}cos(x^{3}) + 81x^{10}sin(x^{3}) + \frac{24sin(x^{3})}{x^{5}} - \frac{24cos(x^{3})}{x^{2}} - 72xsin(x^{3}) - 216x^{4}cos(x^{3}) + 81x^{7}sin(x^{3}) - 288cos(x^{3}) + 4752x^{3}sin(x^{3}) + 5184x^{6}cos(x^{3}) - 972x^{9}sin(x^{3}) - 24tan(x^{2} + 1)sec^{2}(x^{2} + 1) - 96x^{2}sec^{4}(x^{2} + 1) - 192x^{2}tan^{2}(x^{2} + 1)sec^{2}(x^{2} + 1) - 256x^{4}tan(x^{2} + 1)sec^{4}(x^{2} + 1) - 128x^{4}tan^{3}(x^{2} + 1)sec^{2}(x^{2} + 1)\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！