There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ be^{t}a(1) + be^{t}a(2)e^{(-2){(\frac{(x - be^{t}a(3))e^{t}a(4)}{b})}^{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2bae^{t}e^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}} + bae^{t}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2bae^{t}e^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}} + bae^{t}\right)}{dx}\\=&2bae^{t}*0e^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}} + 2bae^{t}e^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}}(\frac{-32a^{2}*2xe^{{t}*{2}}}{b^{2}} - \frac{32a^{2}x^{2}*2e^{t}e^{t}*0}{b^{2}} + \frac{192a^{3}e^{{t}*{3}}}{b} + \frac{192a^{3}x*3e^{{t}*{2}}e^{t}*0}{b} - 288a^{4}*4e^{{t}*{3}}e^{t}*0) + bae^{t}*0\\=&\frac{-128a^{3}xe^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}}e^{{t}*{3}}}{b} + 384a^{4}e^{\frac{-32a^{2}x^{2}e^{{t}*{2}}}{b^{2}} + \frac{192a^{3}xe^{{t}*{3}}}{b} - 288a^{4}e^{{t}*{4}}}e^{{t}*{4}}\\ \end{split}\end{equation} \]

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