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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{((-22{x}^{2} + 46x - 20)a + (2x + 4)b + (-16{x}^{2} - 50x + 36)c + (-20{x}^{2} + 48x - 24)d + (-19{x}^{2} - 48x + 28)e + (-12{x}^{2} - 16)f + (6x - 8)g + (2x + 4)h)}{(41{x}^{2} - 94x + 48)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-22ax^{2}}{(41x^{2} - 94x + 48)} + \frac{46ax}{(41x^{2} - 94x + 48)} - \frac{20a}{(41x^{2} - 94x + 48)} + \frac{2bx}{(41x^{2} - 94x + 48)} + \frac{4b}{(41x^{2} - 94x + 48)} - \frac{16cx^{2}}{(41x^{2} - 94x + 48)} - \frac{50cx}{(41x^{2} - 94x + 48)} + \frac{36c}{(41x^{2} - 94x + 48)} - \frac{20dx^{2}}{(41x^{2} - 94x + 48)} + \frac{48dx}{(41x^{2} - 94x + 48)} - \frac{24d}{(41x^{2} - 94x + 48)} - \frac{19x^{2}e}{(41x^{2} - 94x + 48)} - \frac{48xe}{(41x^{2} - 94x + 48)} + \frac{28e}{(41x^{2} - 94x + 48)} - \frac{12fx^{2}}{(41x^{2} - 94x + 48)} - \frac{16f}{(41x^{2} - 94x + 48)} + \frac{6gx}{(41x^{2} - 94x + 48)} - \frac{8g}{(41x^{2} - 94x + 48)} + \frac{2hx}{(41x^{2} - 94x + 48)} + \frac{4h}{(41x^{2} - 94x + 48)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-22ax^{2}}{(41x^{2} - 94x + 48)} + \frac{46ax}{(41x^{2} - 94x + 48)} - \frac{20a}{(41x^{2} - 94x + 48)} + \frac{2bx}{(41x^{2} - 94x + 48)} + \frac{4b}{(41x^{2} - 94x + 48)} - \frac{16cx^{2}}{(41x^{2} - 94x + 48)} - \frac{50cx}{(41x^{2} - 94x + 48)} + \frac{36c}{(41x^{2} - 94x + 48)} - \frac{20dx^{2}}{(41x^{2} - 94x + 48)} + \frac{48dx}{(41x^{2} - 94x + 48)} - \frac{24d}{(41x^{2} - 94x + 48)} - \frac{19x^{2}e}{(41x^{2} - 94x + 48)} - \frac{48xe}{(41x^{2} - 94x + 48)} + \frac{28e}{(41x^{2} - 94x + 48)} - \frac{12fx^{2}}{(41x^{2} - 94x + 48)} - \frac{16f}{(41x^{2} - 94x + 48)} + \frac{6gx}{(41x^{2} - 94x + 48)} - \frac{8g}{(41x^{2} - 94x + 48)} + \frac{2hx}{(41x^{2} - 94x + 48)} + \frac{4h}{(41x^{2} - 94x + 48)}\right)}{dx}\\=&-22(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})ax^{2} - \frac{22a*2x}{(41x^{2} - 94x + 48)} + 46(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})ax + \frac{46a}{(41x^{2} - 94x + 48)} - 20(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})a + 0 + 2(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})bx + \frac{2b}{(41x^{2} - 94x + 48)} + 4(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})b + 0 - 16(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})cx^{2} - \frac{16c*2x}{(41x^{2} - 94x + 48)} - 50(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})cx - \frac{50c}{(41x^{2} - 94x + 48)} + 36(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})c + 0 - 20(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})dx^{2} - \frac{20d*2x}{(41x^{2} - 94x + 48)} + 48(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})dx + \frac{48d}{(41x^{2} - 94x + 48)} - 24(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})d + 0 - 19(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}e - \frac{19*2xe}{(41x^{2} - 94x + 48)} - \frac{19x^{2}*0}{(41x^{2} - 94x + 48)} - 48(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})xe - \frac{48e}{(41x^{2} - 94x + 48)} - \frac{48x*0}{(41x^{2} - 94x + 48)} + 28(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})e + \frac{28*0}{(41x^{2} - 94x + 48)} - 12(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})fx^{2} - \frac{12f*2x}{(41x^{2} - 94x + 48)} - 16(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})f + 0 + 6(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})gx + \frac{6g}{(41x^{2} - 94x + 48)} - 8(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})g + 0 + 2(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})hx + \frac{2h}{(41x^{2} - 94x + 48)} + 4(\frac{-(41*2x - 94 + 0)}{(41x^{2} - 94x + 48)^{2}})h + 0\\=&\frac{1804ax^{3}}{(41x^{2} - 94x + 48)^{2}} - \frac{5840ax^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{44ax}{(41x^{2} - 94x + 48)} + \frac{5964ax}{(41x^{2} - 94x + 48)^{2}} + \frac{46a}{(41x^{2} - 94x + 48)} - \frac{1880a}{(41x^{2} - 94x + 48)^{2}} - \frac{164bx^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{140bx}{(41x^{2} - 94x + 48)^{2}} + \frac{2b}{(41x^{2} - 94x + 48)} + \frac{376b}{(41x^{2} - 94x + 48)^{2}} + \frac{1312cx^{3}}{(41x^{2} - 94x + 48)^{2}} + \frac{2596cx^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{32cx}{(41x^{2} - 94x + 48)} - \frac{7652cx}{(41x^{2} - 94x + 48)^{2}} - \frac{50c}{(41x^{2} - 94x + 48)} + \frac{3384c}{(41x^{2} - 94x + 48)^{2}} + \frac{1640dx^{3}}{(41x^{2} - 94x + 48)^{2}} - \frac{5816dx^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{40dx}{(41x^{2} - 94x + 48)} + \frac{6480dx}{(41x^{2} - 94x + 48)^{2}} + \frac{48d}{(41x^{2} - 94x + 48)} - \frac{2256d}{(41x^{2} - 94x + 48)^{2}} + \frac{1558x^{3}e}{(41x^{2} - 94x + 48)^{2}} + \frac{2150x^{2}e}{(41x^{2} - 94x + 48)^{2}} - \frac{38xe}{(41x^{2} - 94x + 48)} - \frac{6808xe}{(41x^{2} - 94x + 48)^{2}} - \frac{48e}{(41x^{2} - 94x + 48)} + \frac{2632e}{(41x^{2} - 94x + 48)^{2}} + \frac{984fx^{3}}{(41x^{2} - 94x + 48)^{2}} - \frac{1128fx^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{24fx}{(41x^{2} - 94x + 48)} + \frac{1312fx}{(41x^{2} - 94x + 48)^{2}} - \frac{1504f}{(41x^{2} - 94x + 48)^{2}} - \frac{492gx^{2}}{(41x^{2} - 94x + 48)^{2}} + \frac{1220gx}{(41x^{2} - 94x + 48)^{2}} - \frac{752g}{(41x^{2} - 94x + 48)^{2}} + \frac{6g}{(41x^{2} - 94x + 48)} - \frac{164hx^{2}}{(41x^{2} - 94x + 48)^{2}} - \frac{140hx}{(41x^{2} - 94x + 48)^{2}} + \frac{376h}{(41x^{2} - 94x + 48)^{2}} + \frac{2h}{(41x^{2} - 94x + 48)}\\ \end{split}\end{equation} \]

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