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

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