本次共计算 1 个题目：每一题对 c 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{((-22{x}^{2} + 46x - 20)a + (2x + 4)b + (-16{x}^{2} - 50x + 36 - 20m{x}^{2} + 48mx - 24m)c + (-19{x}^{2} - 48x + 28)e + (-12{x}^{2} - 16)f + (6x - 8)g + (2x + 4)h)}{(41{x}^{2} - 94x + 48)} 关于 c 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-22x^{2}a}{(41x^{2} - 94x + 48)} + \frac{46xa}{(41x^{2} - 94x + 48)} - \frac{20a}{(41x^{2} - 94x + 48)} + \frac{2xb}{(41x^{2} - 94x + 48)} + \frac{4b}{(41x^{2} - 94x + 48)} - \frac{16x^{2}c}{(41x^{2} - 94x + 48)} - \frac{50xc}{(41x^{2} - 94x + 48)} + \frac{36c}{(41x^{2} - 94x + 48)} - \frac{20x^{2}mc}{(41x^{2} - 94x + 48)} + \frac{48xmc}{(41x^{2} - 94x + 48)} - \frac{24mc}{(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{12x^{2}f}{(41x^{2} - 94x + 48)} - \frac{16f}{(41x^{2} - 94x + 48)} + \frac{6xg}{(41x^{2} - 94x + 48)} - \frac{8g}{(41x^{2} - 94x + 48)} + \frac{2xh}{(41x^{2} - 94x + 48)} + \frac{4h}{(41x^{2} - 94x + 48)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-22x^{2}a}{(41x^{2} - 94x + 48)} + \frac{46xa}{(41x^{2} - 94x + 48)} - \frac{20a}{(41x^{2} - 94x + 48)} + \frac{2xb}{(41x^{2} - 94x + 48)} + \frac{4b}{(41x^{2} - 94x + 48)} - \frac{16x^{2}c}{(41x^{2} - 94x + 48)} - \frac{50xc}{(41x^{2} - 94x + 48)} + \frac{36c}{(41x^{2} - 94x + 48)} - \frac{20x^{2}mc}{(41x^{2} - 94x + 48)} + \frac{48xmc}{(41x^{2} - 94x + 48)} - \frac{24mc}{(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{12x^{2}f}{(41x^{2} - 94x + 48)} - \frac{16f}{(41x^{2} - 94x + 48)} + \frac{6xg}{(41x^{2} - 94x + 48)} - \frac{8g}{(41x^{2} - 94x + 48)} + \frac{2xh}{(41x^{2} - 94x + 48)} + \frac{4h}{(41x^{2} - 94x + 48)}\right)}{dc}\\=&-22(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}a + 0 + 46(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xa + 0 - 20(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})a + 0 + 2(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xb + 0 + 4(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})b + 0 - 16(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}c - \frac{16x^{2}}{(41x^{2} - 94x + 48)} - 50(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xc - \frac{50x}{(41x^{2} - 94x + 48)} + 36(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})c + \frac{36}{(41x^{2} - 94x + 48)} - 20(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}mc - \frac{20x^{2}m}{(41x^{2} - 94x + 48)} + 48(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xmc + \frac{48xm}{(41x^{2} - 94x + 48)} - 24(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})mc - \frac{24m}{(41x^{2} - 94x + 48)} - 19(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}e - \frac{19x^{2}*0}{(41x^{2} - 94x + 48)} - 48(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xe - \frac{48x*0}{(41x^{2} - 94x + 48)} + 28(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})e + \frac{28*0}{(41x^{2} - 94x + 48)} - 12(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})x^{2}f + 0 - 16(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})f + 0 + 6(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xg + 0 - 8(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})g + 0 + 2(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})xh + 0 + 4(\frac{-(0 + 0 + 0)}{(41x^{2} - 94x + 48)^{2}})h + 0\\=& - \frac{20x^{2}m}{(41x^{2} - 94x + 48)} + \frac{48xm}{(41x^{2} - 94x + 48)} - \frac{16x^{2}}{(41x^{2} - 94x + 48)} - \frac{50x}{(41x^{2} - 94x + 48)} - \frac{24m}{(41x^{2} - 94x + 48)} + \frac{36}{(41x^{2} - 94x + 48)}\\ \end{split}\end{equation} \]

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