There are 1 questions in this calculation: for each question, the 1 derivative of D is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ GM(2{D}^{2} - {x}^{2}){\frac{1}{({x}^{2} + {D}^{2})}}^{\frac{5}{2}}\ with\ respect\ to\ D：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2GMD^{2}}{(x^{2} + D^{2})^{\frac{5}{2}}} - \frac{GMx^{2}}{(x^{2} + D^{2})^{\frac{5}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2GMD^{2}}{(x^{2} + D^{2})^{\frac{5}{2}}} - \frac{GMx^{2}}{(x^{2} + D^{2})^{\frac{5}{2}}}\right)}{dD}\\=&2(\frac{\frac{-5}{2}(0 + 2D)}{(x^{2} + D^{2})^{\frac{7}{2}}})GMD^{2} + \frac{2GM*2D}{(x^{2} + D^{2})^{\frac{5}{2}}} - (\frac{\frac{-5}{2}(0 + 2D)}{(x^{2} + D^{2})^{\frac{7}{2}}})GMx^{2} + 0\\=&\frac{-10GMD^{3}}{(x^{2} + D^{2})^{\frac{7}{2}}} + \frac{4GMD}{(x^{2} + D^{2})^{\frac{5}{2}}} + \frac{5GMx^{2}D}{(x^{2} + D^{2})^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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