本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(1 - {\frac{1}{4}}^{x})(2x(x + 1)(2x + 1) - 3x)}{18} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{2}{9}x^{3}{\frac{1}{4}}^{x} - \frac{1}{3}x^{2}{\frac{1}{4}}^{x} + \frac{1}{18}x{\frac{1}{4}}^{x} + \frac{1}{3}x^{2} + \frac{2}{9}x^{3} - \frac{1}{18}x\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{2}{9}x^{3}{\frac{1}{4}}^{x} - \frac{1}{3}x^{2}{\frac{1}{4}}^{x} + \frac{1}{18}x{\frac{1}{4}}^{x} + \frac{1}{3}x^{2} + \frac{2}{9}x^{3} - \frac{1}{18}x\right)}{dx}\\=& - \frac{2}{9}*3x^{2}{\frac{1}{4}}^{x} - \frac{2}{9}x^{3}({\frac{1}{4}}^{x}((1)ln(\frac{1}{4}) + \frac{(x)(0)}{(\frac{1}{4})})) - \frac{1}{3}*2x{\frac{1}{4}}^{x} - \frac{1}{3}x^{2}({\frac{1}{4}}^{x}((1)ln(\frac{1}{4}) + \frac{(x)(0)}{(\frac{1}{4})})) + \frac{1}{18} * {\frac{1}{4}}^{x} + \frac{1}{18}x({\frac{1}{4}}^{x}((1)ln(\frac{1}{4}) + \frac{(x)(0)}{(\frac{1}{4})})) + \frac{1}{3}*2x + \frac{2}{9}*3x^{2} - \frac{1}{18}\\=& - \frac{2x^{3}{\frac{1}{4}}^{x}ln(\frac{1}{4})}{9} - \frac{x^{2}{\frac{1}{4}}^{x}ln(\frac{1}{4})}{3} + \frac{x{\frac{1}{4}}^{x}ln(\frac{1}{4})}{18} - \frac{2x^{2}{\frac{1}{4}}^{x}}{3} + \frac{{\frac{1}{4}}^{x}}{18} - \frac{2x{\frac{1}{4}}^{x}}{3} + \frac{2x}{3} + \frac{2x^{2}}{3} - \frac{1}{18}\\ \end{split}\end{equation} \]

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