There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2(2x - 1)ln(2x - 1) - 6x + 6)}{((2x - 1){\frac{1}{(x - 1)}}^{3})} + \frac{2{\frac{1}{(x - 1)}}^{2}}{({(2x - 1)}^{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{2ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{6x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2}{(2x - 1)^{2}(x - 1)^{2}} + \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{4xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{2ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{6x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2}{(2x - 1)^{2}(x - 1)^{2}} + \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\right)}{dx}\\=&4(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})xln(2x - 1) + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{4x(2 + 0)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})(2x - 1)} - 2(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})ln(2x - 1) - \frac{2(2 + 0)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})(2x - 1)} - 6(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})x - \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2(\frac{-2(2 + 0)}{(2x - 1)^{3}})}{(x - 1)^{2}} + \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{(2x - 1)^{2}} + 6(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})\\=&\frac{24x^{2}ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{8xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} - \frac{24xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{8x}{(2x - 1)(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} + \frac{6ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{36x^{2}}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} + \frac{12x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} + \frac{54x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{8}{(2x - 1)^{3}(x - 1)^{2}} - \frac{4}{(x - 1)^{3}(2x - 1)^{2}} - \frac{4}{(2x - 1)(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{18}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{12}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} - \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!