There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{y}{({y}^{2} + {(x - s)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{y}{(y^{2} + x^{2} - 2sx + s^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{y}{(y^{2} + x^{2} - 2sx + s^{2})}\right)}{dx}\\=&(\frac{-(0 + 2x - 2s + 0)}{(y^{2} + x^{2} - 2sx + s^{2})^{2}})y + 0\\=&\frac{-2yx}{(y^{2} + x^{2} - 2sx + s^{2})^{2}} + \frac{2ys}{(y^{2} + x^{2} - 2sx + s^{2})^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2yx}{(y^{2} + x^{2} - 2sx + s^{2})^{2}} + \frac{2ys}{(y^{2} + x^{2} - 2sx + s^{2})^{2}}\right)}{dx}\\=&-2(\frac{-2(0 + 2x - 2s + 0)}{(y^{2} + x^{2} - 2sx + s^{2})^{3}})yx - \frac{2y}{(y^{2} + x^{2} - 2sx + s^{2})^{2}} + 2(\frac{-2(0 + 2x - 2s + 0)}{(y^{2} + x^{2} - 2sx + s^{2})^{3}})ys + 0\\=&\frac{8yx^{2}}{(y^{2} + x^{2} - 2sx + s^{2})^{3}} - \frac{16ysx}{(y^{2} + x^{2} - 2sx + s^{2})^{3}} + \frac{8ys^{2}}{(y^{2} + x^{2} - 2sx + s^{2})^{3}} - \frac{2y}{(y^{2} + x^{2} - 2sx + s^{2})^{2}}\\ \end{split}\end{equation} \]

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