本次共计算 1 个题目:每一题对 x 求 15 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数sin(1 - ({x}^{2} - ln(x))) 关于 x 的 15 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(-x^{2} + ln(x) + 1)\\\\ &\color{blue}{函数的 15 阶导数:} \\=&-461260800xsin(-x^{2} + ln(x) + 1) - 205004800x^{3}cos(-x^{2} + ln(x) + 1) + 527155200xcos(-x^{2} + ln(x) + 1) - \frac{4118400cos(-x^{2} + ln(x) + 1)}{x} + \frac{219419200cos(-x^{2} + ln(x) + 1)}{x^{3}} - \frac{14414400sin(-x^{2} + ln(x) + 1)}{x^{3}} - 1568286720x^{5}sin(-x^{2} + ln(x) + 1) + 2767564800x^{3}sin(-x^{2} + ln(x) + 1) + 1079070720x^{7}cos(-x^{2} + ln(x) + 1) - 2736814080x^{5}cos(-x^{2} + ln(x) + 1) + \frac{120120000cos(-x^{2} + ln(x) + 1)}{x^{5}} + \frac{1316515200sin(-x^{2} + ln(x) + 1)}{x^{5}} + 279552000x^{9}sin(-x^{2} + ln(x) + 1) - 984023040x^{7}sin(-x^{2} + ln(x) + 1) - 32686080x^{11}cos(-x^{2} + ln(x) + 1) + 152821760x^{9}cos(-x^{2} + ln(x) + 1) - \frac{6598956000cos(-x^{2} + ln(x) + 1)}{x^{7}} + \frac{684684000sin(-x^{2} + ln(x) + 1)}{x^{7}} - \frac{3118388000cos(-x^{2} + ln(x) + 1)}{x^{9}} - \frac{26461344000sin(-x^{2} + ln(x) + 1)}{x^{9}} + \frac{79534182000cos(-x^{2} + ln(x) + 1)}{x^{11}} - \frac{10559094000sin(-x^{2} + ln(x) + 1)}{x^{11}} - 1720320x^{13}sin(-x^{2} + ln(x) + 1) + 10321920x^{11}sin(-x^{2} + ln(x) + 1) + 32768x^{15}cos(-x^{2} + ln(x) + 1) - 245760x^{13}cos(-x^{2} + ln(x) + 1) + \frac{23705058000cos(-x^{2} + ln(x) + 1)}{x^{13}} + \frac{159275844000sin(-x^{2} + ln(x) + 1)}{x^{13}} + \frac{26495469000sin(-x^{2} + ln(x) + 1)}{x^{15}} - \frac{159300557000cos(-x^{2} + ln(x) + 1)}{x^{15}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!