There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{1176e^{\frac{3x}{10}}}{(5sqrt(3136e^{\frac{3x}{10}} + 4000))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1176}{5}e^{\frac{3}{10}x}}{sqrt(3136e^{\frac{3}{10}x} + 4000)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1176}{5}e^{\frac{3}{10}x}}{sqrt(3136e^{\frac{3}{10}x} + 4000)}\right)}{dx}\\=&\frac{\frac{1176}{5}e^{\frac{3}{10}x}*\frac{3}{10}}{sqrt(3136e^{\frac{3}{10}x} + 4000)} + \frac{\frac{1176}{5}e^{\frac{3}{10}x}*-(3136e^{\frac{3}{10}x}*\frac{3}{10} + 0)*\frac{1}{2}}{(3136e^{\frac{3}{10}x} + 4000)(3136e^{\frac{3}{10}x} + 4000)^{\frac{1}{2}}}\\=&\frac{1764e^{\frac{3}{10}x}}{25sqrt(3136e^{\frac{3}{10}x} + 4000)} - \frac{2765952e^{{\frac{3}{10}x}*{2}}}{25(3136e^{\frac{3}{10}x} + 4000)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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