本次共计算 1 个题目:每一题对 x 求 3 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数cos(tan(sec(sin(x)))) 关于 x 的 3 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( cos(tan(sec(sin(x))))\right)}{dx}\\=&-sin(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))\\=&-sin(tan(sec(sin(x))))cos(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( -sin(tan(sec(sin(x))))cos(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))\right)}{dx}\\=&-cos(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))cos(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))*-sin(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos(x)sec^{2}(sin(x))(cos(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos(x)tan(sin(x))*2sec^{2}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)sec(sin(x)) - sin(tan(sec(sin(x))))cos(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)\\=&-cos^{2}(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) + sin(x)sin(tan(sec(sin(x))))tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)sec^{3}(sin(x))sec^{2}(sec(sin(x))) - 2sin(tan(sec(sin(x))))cos^{2}(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( -cos^{2}(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) + sin(x)sin(tan(sec(sin(x))))tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)sec^{3}(sin(x))sec^{2}(sec(sin(x))) - 2sin(tan(sec(sin(x))))cos^{2}(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))\right)}{dx}\\=&--2cos(x)sin(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) - cos^{2}(x)*-sin(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))tan^{2}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) - cos^{2}(x)cos(tan(sec(sin(x))))*2tan(sin(x))sec^{2}(sin(x))(cos(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) - cos^{2}(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))*4sec^{4}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)sec^{2}(sin(x)) - cos^{2}(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{4}(sec(sin(x)))*2sec^{2}(sin(x))tan(sin(x))cos(x) + cos(x)sin(tan(sec(sin(x))))tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) + sin(x)cos(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) + sin(x)sin(tan(sec(sin(x))))sec^{2}(sin(x))(cos(x))sec^{2}(sec(sin(x)))sec(sin(x)) + sin(x)sin(tan(sec(sin(x))))tan(sin(x))*2sec^{2}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)sec(sin(x)) + sin(x)sin(tan(sec(sin(x))))tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x) - cos(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))cos^{2}(x)sec^{3}(sin(x))sec^{2}(sec(sin(x))) - sin(tan(sec(sin(x))))*-2cos(x)sin(x)sec^{3}(sin(x))sec^{2}(sec(sin(x))) - sin(tan(sec(sin(x))))cos^{2}(x)*3sec^{3}(sin(x))tan(sin(x))cos(x)sec^{2}(sec(sin(x))) - sin(tan(sec(sin(x))))cos^{2}(x)sec^{3}(sin(x))*2sec^{2}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x) - 2cos(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))cos^{2}(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))*-2cos(x)sin(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{2}(x)sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{2}(x)tan(sec(sin(x)))*2tan(sin(x))sec^{2}(sin(x))(cos(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{2}(x)tan(sec(sin(x)))tan^{2}(sin(x))*2sec^{2}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{2}(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))*2sec^{2}(sin(x))tan(sin(x))cos(x) - cos(tan(sec(sin(x))))sec^{2}(sec(sin(x)))(sec(sin(x))tan(sin(x))cos(x))cos^{2}(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))*-2cos(x)sin(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)*2tan(sin(x))sec^{2}(sin(x))(cos(x))sec^{2}(sec(sin(x)))sec(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)tan^{2}(sin(x))*2sec^{2}(sec(sin(x)))tan(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)sec(sin(x)) - sin(tan(sec(sin(x))))cos^{2}(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x))tan(sin(x))cos(x)\\=&2sin(x)cos(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) + sin(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))sec^{3}(sin(x))sec^{6}(sec(sin(x))) - 2cos(tan(sec(sin(x))))cos^{3}(x)tan(sin(x))sec^{4}(sin(x))sec^{4}(sec(sin(x))) - 2cos^{3}(x)cos(tan(sec(sin(x))))tan^{3}(sin(x))tan(sec(sin(x)))sec^{3}(sin(x))sec^{4}(sec(sin(x))) - 2cos(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) + sin(tan(sec(sin(x))))cos(x)tan(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) + sin(x)cos(x)cos(tan(sec(sin(x))))tan^{2}(sin(x))sec^{2}(sin(x))sec^{4}(sec(sin(x))) + 3sin(x)sin(tan(sec(sin(x))))cos(x)sec^{3}(sin(x))sec^{2}(sec(sin(x))) + 6sin(x)sin(tan(sec(sin(x))))cos(x)tan(sec(sin(x)))tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) + 3sin(x)sin(tan(sec(sin(x))))cos(x)tan^{2}(sin(x))sec^{2}(sec(sin(x)))sec(sin(x)) - cos^{3}(x)cos(tan(sec(sin(x))))tan(sin(x))sec^{4}(sin(x))sec^{4}(sec(sin(x))) - 5sin(tan(sec(sin(x))))cos^{3}(x)tan(sin(x))sec^{3}(sin(x))sec^{2}(sec(sin(x))) - 2sin(tan(sec(sin(x))))cos^{3}(x)tan(sin(x))tan(sec(sin(x)))sec^{2}(sec(sin(x)))sec^{4}(sin(x)) - 4cos^{3}(x)cos(tan(sec(sin(x))))tan(sec(sin(x)))tan^{3}(sin(x))sec^{4}(sec(sin(x)))sec^{3}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))sec^{3}(sin(x))sec^{4}(sec(sin(x))) - 4sin(tan(sec(sin(x))))cos^{3}(x)tan(sin(x))tan(sec(sin(x)))sec^{4}(sin(x))sec^{2}(sec(sin(x))) - 4sin(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))tan^{2}(sec(sin(x)))sec^{2}(sec(sin(x)))sec^{3}(sin(x)) - 4sin(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))tan(sec(sin(x)))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - cos^{3}(x)cos(tan(sec(sin(x))))tan^{3}(sin(x))sec^{4}(sec(sin(x)))sec^{2}(sin(x)) - 2sin(tan(sec(sin(x))))cos^{3}(x)tan(sec(sin(x)))tan^{3}(sin(x))sec^{2}(sec(sin(x)))sec^{2}(sin(x)) - sin(tan(sec(sin(x))))cos^{3}(x)tan^{3}(sin(x))sec^{2}(sec(sin(x)))sec(sin(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!