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

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