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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{X}{(ln(10)x)} + \frac{lg(x)}{sqrt(1 - xx)}){\frac{1}{X}}^{2} 关于 X 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{xXln(10)} + \frac{lg(x)}{X^{2}sqrt(-x^{2} + 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{xXln(10)} + \frac{lg(x)}{X^{2}sqrt(-x^{2} + 1)}\right)}{dX}\\=&\frac{-1}{xX^{2}ln(10)} + \frac{-0}{xXln^{2}(10)(10)} + \frac{-2lg(x)}{X^{3}sqrt(-x^{2} + 1)} + \frac{0}{X^{2}ln{10}(x)sqrt(-x^{2} + 1)} + \frac{lg(x)*-(0 + 0)*\frac{1}{2}}{X^{2}(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-1}{xX^{2}ln(10)} - \frac{2lg(x)}{X^{3}sqrt(-x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-1}{xX^{2}ln(10)} - \frac{2lg(x)}{X^{3}sqrt(-x^{2} + 1)}\right)}{dX}\\=&\frac{--2}{xX^{3}ln(10)} - \frac{-0}{xX^{2}ln^{2}(10)(10)} - \frac{2*-3lg(x)}{X^{4}sqrt(-x^{2} + 1)} - \frac{2*0}{X^{3}ln{10}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)*-(0 + 0)*\frac{1}{2}}{X^{3}(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{2}{xX^{3}ln(10)} + \frac{6lg(x)}{X^{4}sqrt(-x^{2} + 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2}{xX^{3}ln(10)} + \frac{6lg(x)}{X^{4}sqrt(-x^{2} + 1)}\right)}{dX}\\=&\frac{2*-3}{xX^{4}ln(10)} + \frac{2*-0}{xX^{3}ln^{2}(10)(10)} + \frac{6*-4lg(x)}{X^{5}sqrt(-x^{2} + 1)} + \frac{6*0}{X^{4}ln{10}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)*-(0 + 0)*\frac{1}{2}}{X^{4}(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-6}{xX^{4}ln(10)} - \frac{24lg(x)}{X^{5}sqrt(-x^{2} + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6}{xX^{4}ln(10)} - \frac{24lg(x)}{X^{5}sqrt(-x^{2} + 1)}\right)}{dX}\\=&\frac{-6*-4}{xX^{5}ln(10)} - \frac{6*-0}{xX^{4}ln^{2}(10)(10)} - \frac{24*-5lg(x)}{X^{6}sqrt(-x^{2} + 1)} - \frac{24*0}{X^{5}ln{10}(x)sqrt(-x^{2} + 1)} - \frac{24lg(x)*-(0 + 0)*\frac{1}{2}}{X^{5}(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{24}{xX^{5}ln(10)} + \frac{120lg(x)}{X^{6}sqrt(-x^{2} + 1)}\\ \end{split}\end{equation} \]

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