本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数{(1 + sin(3){x}^{2})}^{4} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{8}sin^{4}(3) + 4x^{6}sin^{3}(3) + 6x^{4}sin^{2}(3) + 4x^{2}sin(3) + 1\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x^{8}sin^{4}(3) + 4x^{6}sin^{3}(3) + 6x^{4}sin^{2}(3) + 4x^{2}sin(3) + 1\right)}{dx}\\=&8x^{7}sin^{4}(3) + x^{8}*4sin^{3}(3)cos(3)*0 + 4*6x^{5}sin^{3}(3) + 4x^{6}*3sin^{2}(3)cos(3)*0 + 6*4x^{3}sin^{2}(3) + 6x^{4}*2sin(3)cos(3)*0 + 4*2xsin(3) + 4x^{2}cos(3)*0 + 0\\=&8x^{7}sin^{4}(3) + 24x^{5}sin^{3}(3) + 24x^{3}sin^{2}(3) + 8xsin(3)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 8x^{7}sin^{4}(3) + 24x^{5}sin^{3}(3) + 24x^{3}sin^{2}(3) + 8xsin(3)\right)}{dx}\\=&8*7x^{6}sin^{4}(3) + 8x^{7}*4sin^{3}(3)cos(3)*0 + 24*5x^{4}sin^{3}(3) + 24x^{5}*3sin^{2}(3)cos(3)*0 + 24*3x^{2}sin^{2}(3) + 24x^{3}*2sin(3)cos(3)*0 + 8sin(3) + 8xcos(3)*0\\=&56x^{6}sin^{4}(3) + 120x^{4}sin^{3}(3) + 72x^{2}sin^{2}(3) + 8sin(3)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!