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。\[ \begin{equation}\begin{split}【1/1】求函数{sin(x)}^{100} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin^{100}(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( sin^{100}(x)\right)}{dx}\\=&100sin^{99}(x)cos(x)\\=&100sin^{99}(x)cos(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 100sin^{99}(x)cos(x)\right)}{dx}\\=&100*99sin^{98}(x)cos(x)cos(x) + 100sin^{99}(x)*-sin(x)\\=&9900sin^{98}(x)cos^{2}(x) - 100sin^{100}(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( 9900sin^{98}(x)cos^{2}(x) - 100sin^{100}(x)\right)}{dx}\\=&9900*98sin^{97}(x)cos(x)cos^{2}(x) + 9900sin^{98}(x)*-2cos(x)sin(x) - 100*100sin^{99}(x)cos(x)\\=&970200sin^{97}(x)cos^{3}(x) - 29800sin^{99}(x)cos(x)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 970200sin^{97}(x)cos^{3}(x) - 29800sin^{99}(x)cos(x)\right)}{dx}\\=&970200*97sin^{96}(x)cos(x)cos^{3}(x) + 970200sin^{97}(x)*-3cos^{2}(x)sin(x) - 29800*99sin^{98}(x)cos(x)cos(x) - 29800sin^{99}(x)*-sin(x)\\=&94109400sin^{96}(x)cos^{4}(x) - 5860800sin^{98}(x)cos^{2}(x) + 29800sin^{100}(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!