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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{e}^{lg(2x)}(sin(3)x(tan(4)x) - cos(3x - 2))}{({2}^{x} + {x}^{e^{sh(x) - csch(x)(\frac{1}{x})}})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}{e}^{lg(2x)}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} - \frac{{e}^{lg(2x)}cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}{e}^{lg(2x)}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} - \frac{{e}^{lg(2x)}cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})}\right)}{dx}\\=&(\frac{-(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + ({x}^{e^{sh(x) - \frac{csch(x)}{x}}}((e^{sh(x) - \frac{csch(x)}{x}}(ch(x) - \frac{-csch(x)}{x^{2}} - \frac{-csch(x)coth(x)}{x}))ln(x) + \frac{(e^{sh(x) - \frac{csch(x)}{x}})(1)}{(x)})))}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}})x^{2}{e}^{lg(2x)}sin(3)tan(4) + \frac{2x{e}^{lg(2x)}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} + \frac{x^{2}({e}^{lg(2x)}((\frac{2}{ln{10}(2x)})ln(e) + \frac{(lg(2x))(0)}{(e)}))sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} + \frac{x^{2}{e}^{lg(2x)}cos(3)*0tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} + \frac{x^{2}{e}^{lg(2x)}sin(3)sec^{2}(4)(0)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} - (\frac{-(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + ({x}^{e^{sh(x) - \frac{csch(x)}{x}}}((e^{sh(x) - \frac{csch(x)}{x}}(ch(x) - \frac{-csch(x)}{x^{2}} - \frac{-csch(x)coth(x)}{x}))ln(x) + \frac{(e^{sh(x) - \frac{csch(x)}{x}})(1)}{(x)})))}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}}){e}^{lg(2x)}cos(3x - 2) - \frac{({e}^{lg(2x)}((\frac{2}{ln{10}(2x)})ln(e) + \frac{(lg(2x))(0)}{(e)}))cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} - \frac{{e}^{lg(2x)}*-sin(3x - 2)(3 + 0)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})}\\=&\frac{-x^{2}{2}^{x}{e}^{lg(2x)}ln(2)sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} - \frac{x^{2}{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)sin(3)tan(4)ch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} - \frac{{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)sin(3)tan(4)csch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} - \frac{x{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)sin(3)tan(4)coth(x)csch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} - \frac{x{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} + \frac{2x{e}^{lg(2x)}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})} + \frac{x{e}^{lg(2x)}sin(3)tan(4)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})ln{10}} + \frac{{2}^{x}{e}^{lg(2x)}ln(2)cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} + \frac{{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)cos(3x - 2)ch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}} + \frac{{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)cos(3x - 2)csch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}x^{2}} + \frac{{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}ln(x)cos(3x - 2)coth(x)csch(x)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}x} + \frac{{x}^{e^{sh(x) - \frac{csch(x)}{x}}}{e}^{lg(2x)}e^{sh(x) - \frac{csch(x)}{x}}cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})^{2}x} - \frac{{e}^{lg(2x)}cos(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})xln{10}} + \frac{3{e}^{lg(2x)}sin(3x - 2)}{({2}^{x} + {x}^{e^{sh(x) - \frac{csch(x)}{x}}})}\\ \end{split}\end{equation} \]

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