本次共计算 1 个题目：每一题对 x 求 15 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{x}^{(\frac{2}{3})} + \frac{e{(π - {x}^{2})}^{\frac{1}{2}}sin(8πx)}{3} 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{3}(π - x^{2})^{\frac{1}{2}}esin(8πx) + x^{\frac{2}{3}}\\\\ &\color{blue}{函数的 15 阶导数：} \\=& - \frac{71152682225625x^{15}esin(8πx)}{(π - x^{2})^{\frac{29}{2}}} - \frac{276704875321875x^{13}esin(8πx)}{(π - x^{2})^{\frac{27}{2}}} - \frac{316234143225000πx^{14}ecos(8πx)}{(π - x^{2})^{\frac{27}{2}}} - \frac{431659605502125x^{11}esin(8πx)}{(π - x^{2})^{\frac{25}{2}}} - \frac{1151092281339000πx^{12}ecos(8πx)}{(π - x^{2})^{\frac{25}{2}}} + \frac{708364480824000π^{2}x^{13}esin(8πx)}{(π - x^{2})^{\frac{25}{2}}} - \frac{344076497139375x^{9}esin(8πx)}{(π - x^{2})^{\frac{23}{2}}} - \frac{1651567186269000πx^{10}ecos(8πx)}{(π - x^{2})^{\frac{23}{2}}} + \frac{2402279543664000π^{2}x^{11}esin(8πx)}{(π - x^{2})^{\frac{23}{2}}} + \frac{1067679797184000π^{3}x^{12}ecos(8πx)}{(π - x^{2})^{\frac{23}{2}}} - \frac{147461355916875x^{7}esin(8πx)}{(π - x^{2})^{\frac{21}{2}}} - \frac{1179690847335000πx^{8}ecos(8πx)}{(π - x^{2})^{\frac{21}{2}}} + \frac{3145842259560000π^{2}x^{9}esin(8πx)}{(π - x^{2})^{\frac{21}{2}}} + \frac{3355565076864000π^{3}x^{10}ecos(8πx)}{(π - x^{2})^{\frac{21}{2}}} - \frac{1220205482496000π^{4}x^{11}esin(8πx)}{(π - x^{2})^{\frac{21}{2}}} - \frac{32596720781625x^{5}esin(8πx)}{(π - x^{2})^{\frac{19}{2}}} - \frac{434622943755000πx^{6}ecos(8πx)}{(π - x^{2})^{\frac{19}{2}}} + \frac{1986847742880000π^{2}x^{7}esin(8πx)}{(π - x^{2})^{\frac{19}{2}}} + \frac{3973695485760000π^{3}x^{8}ecos(8πx)}{(π - x^{2})^{\frac{19}{2}}} - \frac{3532173765120000π^{4}x^{9}esin(8πx)}{(π - x^{2})^{\frac{19}{2}}} - \frac{1130295604838400π^{5}x^{10}ecos(8πx)}{(π - x^{2})^{\frac{19}{2}}} - \frac{3195756939375x^{3}esin(8πx)}{(π - x^{2})^{\frac{17}{2}}} - \frac{76698166545000πx^{4}ecos(8πx)}{(π - x^{2})^{\frac{17}{2}}} + \frac{613585332360000π^{2}x^{5}esin(8πx)}{(π - x^{2})^{\frac{17}{2}}} + \frac{2181636737280000π^{3}x^{6}ecos(8πx)}{(π - x^{2})^{\frac{17}{2}}} - \frac{3739948692480000π^{4}x^{7}esin(8πx)}{(π - x^{2})^{\frac{17}{2}}} - \frac{2991958953984000π^{5}x^{8}ecos(8πx)}{(π - x^{2})^{\frac{17}{2}}} + \frac{886506356736000π^{6}x^{9}esin(8πx)}{(π - x^{2})^{\frac{17}{2}}} - \frac{91307341125xesin(8πx)}{(π - x^{2})^{\frac{15}{2}}} - \frac{5113211103000πx^{2}ecos(8πx)}{(π - x^{2})^{\frac{15}{2}}} + \frac{81811377648000π^{2}x^{3}esin(8πx)}{(π - x^{2})^{\frac{15}{2}}} + \frac{545409184320000π^{3}x^{4}ecos(8πx)}{(π - x^{2})^{\frac{15}{2}}} - \frac{1745309389824000π^{4}x^{5}esin(8πx)}{(π - x^{2})^{\frac{15}{2}}} - \frac{2792495023718400π^{5}x^{6}ecos(8πx)}{(π - x^{2})^{\frac{15}{2}}} + \frac{2127615256166400π^{6}x^{7}esin(8πx)}{(π - x^{2})^{\frac{15}{2}}} + \frac{607890073190400π^{7}x^{8}ecos(8πx)}{(π - x^{2})^{\frac{15}{2}}} - \frac{56189133000πecos(8πx)}{(π - x^{2})^{\frac{13}{2}}} + \frac{3146591448000π^{2}xesin(8πx)}{(π - x^{2})^{\frac{13}{2}}} + \frac{50345463168000π^{3}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{13}{2}}} - \frac{335636421120000π^{4}x^{3}esin(8πx)}{(π - x^{2})^{\frac{13}{2}}} - \frac{1074036547584000π^{5}x^{4}ecos(8πx)}{(π - x^{2})^{\frac{13}{2}}} + \frac{1718458476134400π^{6}x^{5}esin(8πx)}{(π - x^{2})^{\frac{13}{2}}} + \frac{1309301696102400π^{7}x^{6}ecos(8πx)}{(π - x^{2})^{\frac{13}{2}}} - \frac{374086198886400π^{8}x^{7}esin(8πx)}{(π - x^{2})^{\frac{13}{2}}} + \frac{762810048000π^{3}ecos(8πx)}{(π - x^{2})^{\frac{11}{2}}} - \frac{18307441152000π^{4}xesin(8πx)}{(π - x^{2})^{\frac{11}{2}}} - \frac{146459529216000π^{5}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{11}{2}}} + \frac{520744992768000π^{6}x^{3}esin(8πx)}{(π - x^{2})^{\frac{11}{2}}} + \frac{892705701888000π^{7}x^{4}ecos(8πx)}{(π - x^{2})^{\frac{11}{2}}} - \frac{714164561510400π^{8}x^{5}esin(8πx)}{(π - x^{2})^{\frac{11}{2}}} - \frac{211604314521600π^{9}x^{6}ecos(8πx)}{(π - x^{2})^{\frac{11}{2}}} - \frac{3254656204800π^{5}ecos(8πx)}{(π - x^{2})^{\frac{9}{2}}} + \frac{43395416064000π^{6}xesin(8πx)}{(π - x^{2})^{\frac{9}{2}}} + \frac{198379044864000π^{7}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{9}{2}}} - \frac{396758089728000π^{8}x^{3}esin(8πx)}{(π - x^{2})^{\frac{9}{2}}} - \frac{352673857536000π^{9}x^{4}ecos(8πx)}{(π - x^{2})^{\frac{9}{2}}} + \frac{112855634411520π^{10}x^{5}esin(8πx)}{(π - x^{2})^{\frac{9}{2}}} + \frac{7084965888000π^{7}ecos(8πx)}{(π - x^{2})^{\frac{7}{2}}} - \frac{56679727104000π^{8}xesin(8πx)}{(π - x^{2})^{\frac{7}{2}}} - \frac{151145938944000π^{9}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{7}{2}}} + \frac{161222334873600π^{10}x^{3}esin(8πx)}{(π - x^{2})^{\frac{7}{2}}} + \frac{58626303590400π^{11}x^{4}ecos(8πx)}{(π - x^{2})^{\frac{7}{2}}} - \frac{10076395929600π^{9}ecos(8πx)}{(π - x^{2})^{\frac{5}{2}}} + \frac{48366700462080π^{10}xesin(8πx)}{(π - x^{2})^{\frac{5}{2}}} + \frac{70351564308480π^{11}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{5}{2}}} - \frac{31267361914880π^{12}x^{3}esin(8πx)}{(π - x^{2})^{\frac{5}{2}}} + \frac{11725260718080π^{11}ecos(8πx)}{(π - x^{2})^{\frac{3}{2}}} - \frac{31267361914880π^{12}xesin(8πx)}{(π - x^{2})^{\frac{3}{2}}} - \frac{19241453486080π^{13}x^{2}ecos(8πx)}{(π - x^{2})^{\frac{3}{2}}} - \frac{19241453486080π^{13}ecos(8πx)}{(π - x^{2})^{\frac{1}{2}}} + \frac{21990232555520π^{14}xesin(8πx)}{(π - x^{2})^{\frac{1}{2}}} - \frac{35184372088832(π - x^{2})^{\frac{1}{2}}π^{15}ecos(8πx)}{3} + \frac{53165268316160000}{14348907x^{\frac{43}{3}}}\\ \end{split}\end{equation} \]

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