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

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