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。\[ \begin{equation}\begin{split}【1/1】求函数{{x}^{15600}}^{20000} + 2{x}^{5000}({x}^{3000000000000000}) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 2x^{3000000000005000} + x^{312000000}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 2x^{3000000000005000} + x^{312000000}\right)}{dx}\\=&2*3000000000005000x^{3000000000004999} + 312000000x^{311999999}\\=&6000000000010000x^{3000000000004999} + 312000000x^{311999999}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 6000000000010000x^{3000000000004999} + 312000000x^{311999999}\right)}{dx}\\=&6000000000010000*3000000000004999x^{3000000000004998} + 312000000*311999999x^{311999998}\\=&3805044275868322160x^{3000000000004998} + 97343999688000000x^{311999998}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( 3805044275868322160x^{3000000000004998} + 97343999688000000x^{311999998}\right)}{dx}\\=&3805044275868322160*3000000000004998x^{3000000000004997} + 97343999688000000*311999998x^{311999997}\\=&2539808964803477664x^{3000000000004997} - 477541837571785728x^{311999997}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 2539808964803477664x^{3000000000004997} - 477541837571785728x^{311999997}\right)}{dx}\\=&2539808964803477664*3000000000004997x^{3000000000004996} - 477541837571785728*311999997x^{311999996}\\=& - 7634917132527078624x^{3000000000004996} + 8721495254313176064x^{311999996}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!