There are 1 questions in this calculation: for each question, the 1 derivative of m is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(4m + 3{m}^{(\frac{3}{2})})}{(2{(1 + {m}^{\frac{1}{2}})}^{2})}\ with\ respect\ to\ m：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2m}{(m^{\frac{1}{2}} + 1)^{2}} + \frac{\frac{3}{2}m^{\frac{3}{2}}}{(m^{\frac{1}{2}} + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2m}{(m^{\frac{1}{2}} + 1)^{2}} + \frac{\frac{3}{2}m^{\frac{3}{2}}}{(m^{\frac{1}{2}} + 1)^{2}}\right)}{dm}\\=&2(\frac{-2(\frac{\frac{1}{2}}{m^{\frac{1}{2}}} + 0)}{(m^{\frac{1}{2}} + 1)^{3}})m + \frac{2}{(m^{\frac{1}{2}} + 1)^{2}} + \frac{3}{2}(\frac{-2(\frac{\frac{1}{2}}{m^{\frac{1}{2}}} + 0)}{(m^{\frac{1}{2}} + 1)^{3}})m^{\frac{3}{2}} + \frac{\frac{3}{2}*\frac{3}{2}m^{\frac{1}{2}}}{(m^{\frac{1}{2}} + 1)^{2}}\\=&\frac{-2m^{\frac{1}{2}}}{(m^{\frac{1}{2}} + 1)^{3}} - \frac{3m}{2(m^{\frac{1}{2}} + 1)^{3}} + \frac{9m^{\frac{1}{2}}}{4(m^{\frac{1}{2}} + 1)^{2}} + \frac{2}{(m^{\frac{1}{2}} + 1)^{2}}\\ \end{split}\end{equation} \]

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