There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ Aln({({x}^{2} + {z}^{2})}^{\frac{1}{2}} + z)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = Aln((x^{2} + z^{2})^{\frac{1}{2}} + z)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( Aln((x^{2} + z^{2})^{\frac{1}{2}} + z)\right)}{dx}\\=&\frac{A((\frac{\frac{1}{2}(2x + 0)}{(x^{2} + z^{2})^{\frac{1}{2}}}) + 0)}{((x^{2} + z^{2})^{\frac{1}{2}} + z)}\\=&\frac{Ax}{((x^{2} + z^{2})^{\frac{1}{2}} + z)(x^{2} + z^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{Ax}{((x^{2} + z^{2})^{\frac{1}{2}} + z)(x^{2} + z^{2})^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(\frac{-((\frac{\frac{1}{2}(2x + 0)}{(x^{2} + z^{2})^{\frac{1}{2}}}) + 0)}{((x^{2} + z^{2})^{\frac{1}{2}} + z)^{2}})Ax}{(x^{2} + z^{2})^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + z^{2})^{\frac{3}{2}}})Ax}{((x^{2} + z^{2})^{\frac{1}{2}} + z)} + \frac{A}{((x^{2} + z^{2})^{\frac{1}{2}} + z)(x^{2} + z^{2})^{\frac{1}{2}}}\\=&\frac{-Ax^{2}}{((x^{2} + z^{2})^{\frac{1}{2}} + z)^{2}(x^{2} + z^{2})} - \frac{Ax^{2}}{((x^{2} + z^{2})^{\frac{1}{2}} + z)(x^{2} + z^{2})^{\frac{3}{2}}} + \frac{A}{((x^{2} + z^{2})^{\frac{1}{2}} + z)(x^{2} + z^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !