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