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

Your problem has not been solved here? Please take a look at the  hot problems ！