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