本次共计算 1 个题目:每一题对 n 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数(8n - 8){(sqrt(n - \frac{47}{10} + \frac{14}{n}))}^{8} - (8{n}^{2} - 36n + 76){(sqrt(n - \frac{47}{10} + \frac{14}{n}))}^{6} - 12(sqrt(2))(n - 1){(sqrt(n - \frac{47}{10} + \frac{14}{n}))}^{5} 关于 n 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - 12nsqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} + 12sqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} - 8n^{2}sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + 36nsqrt(n + \frac{14}{n} - \frac{47}{10})^{6} - 76sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + 8nsqrt(n + \frac{14}{n} - \frac{47}{10})^{8} - 8sqrt(n + \frac{14}{n} - \frac{47}{10})^{8}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( - 12nsqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} + 12sqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} - 8n^{2}sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + 36nsqrt(n + \frac{14}{n} - \frac{47}{10})^{6} - 76sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + 8nsqrt(n + \frac{14}{n} - \frac{47}{10})^{8} - 8sqrt(n + \frac{14}{n} - \frac{47}{10})^{8}\right)}{dn}\\=& - 12sqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} - 12n*0*\frac{1}{2}*2^{\frac{1}{2}}sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} - \frac{12nsqrt(2)*5(n + \frac{14}{n} - \frac{47}{10})^{2}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} + 12*0*\frac{1}{2}*2^{\frac{1}{2}}sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} + \frac{12sqrt(2)*5(n + \frac{14}{n} - \frac{47}{10})^{2}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} - 8*2nsqrt(n + \frac{14}{n} - \frac{47}{10})^{6} - \frac{8n^{2}*6(n + \frac{14}{n} - \frac{47}{10})^{\frac{5}{2}}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} + 36sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + \frac{36n*6(n + \frac{14}{n} - \frac{47}{10})^{\frac{5}{2}}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} - \frac{76*6(n + \frac{14}{n} - \frac{47}{10})^{\frac{5}{2}}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} + 8sqrt(n + \frac{14}{n} - \frac{47}{10})^{8} + \frac{8n*8(n + \frac{14}{n} - \frac{47}{10})^{\frac{7}{2}}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}} - \frac{8*8(n + \frac{14}{n} - \frac{47}{10})^{\frac{7}{2}}(1 + \frac{14*-1}{n^{2}} + 0)*\frac{1}{2}}{(n + \frac{14}{n} - \frac{47}{10})^{\frac{1}{2}}}\\=& - 12sqrt(2)sqrt(n + \frac{14}{n} - \frac{47}{10})^{5} - 30(n + \frac{14}{n} - \frac{47}{10})^{\frac{3}{2}}nsqrt(2) + \frac{420(n + \frac{14}{n} - \frac{47}{10})^{\frac{3}{2}}sqrt(2)}{n} + 30(n + \frac{14}{n} - \frac{47}{10})^{\frac{3}{2}}sqrt(2) - \frac{420(n + \frac{14}{n} - \frac{47}{10})^{\frac{3}{2}}sqrt(2)}{n^{2}} - 16nsqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + 8n^{4} + \frac{33962n^{2}}{25} - \frac{748n^{3}}{5} - \frac{826857n}{125} + \frac{4520278}{125n} + \frac{27823376}{25n^{3}} - \frac{43271858}{125n^{2}} - \frac{9208864}{5n^{4}} + 36sqrt(n + \frac{14}{n} - \frac{47}{10})^{6} + \frac{1229312}{n^{5}} + 8sqrt(n + \frac{14}{n} - \frac{47}{10})^{8} + \frac{1692107}{125}\\ \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!