There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(({(\frac{1}{2})}^{(\frac{3x}{2})}) - (\frac{(2x - 1)}{(2x + 1)}))}{(({(\frac{1}{2})}^{(\frac{3}{(2n - 2)})}) - (\frac{(2x - 3)}{(2x - 1)}))}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{\frac{1}{2}}^{(\frac{3}{2}x)}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} - \frac{2x}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{1}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{{\frac{1}{2}}^{(\frac{3}{2}x)}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} - \frac{2x}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{1}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})}\right)}{dx}\\=&(\frac{-(({\frac{1}{2}}^{(\frac{3}{(2n - 2)})}((3(\frac{-(0 + 0)}{(2n - 2)^{2}}))ln(\frac{1}{2}) + \frac{(\frac{3}{(2n - 2)})(0)}{(\frac{1}{2})})) - 2(\frac{-(2 + 0)}{(2x - 1)^{2}})x - \frac{2}{(2x - 1)} + 3(\frac{-(2 + 0)}{(2x - 1)^{2}}))}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}}){\frac{1}{2}}^{(\frac{3}{2}x)} + \frac{({\frac{1}{2}}^{(\frac{3}{2}x)}((\frac{3}{2})ln(\frac{1}{2}) + \frac{(\frac{3}{2}x)(0)}{(\frac{1}{2})}))}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} - \frac{2(\frac{-(2 + 0)}{(2x + 1)^{2}})x}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} - \frac{2(\frac{-(({\frac{1}{2}}^{(\frac{3}{(2n - 2)})}((3(\frac{-(0 + 0)}{(2n - 2)^{2}}))ln(\frac{1}{2}) + \frac{(\frac{3}{(2n - 2)})(0)}{(\frac{1}{2})})) - 2(\frac{-(2 + 0)}{(2x - 1)^{2}})x - \frac{2}{(2x - 1)} + 3(\frac{-(2 + 0)}{(2x - 1)^{2}}))}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}})x}{(2x + 1)} - \frac{2}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{(\frac{-(2 + 0)}{(2x + 1)^{2}})}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{(\frac{-(({\frac{1}{2}}^{(\frac{3}{(2n - 2)})}((3(\frac{-(0 + 0)}{(2n - 2)^{2}}))ln(\frac{1}{2}) + \frac{(\frac{3}{(2n - 2)})(0)}{(\frac{1}{2})})) - 2(\frac{-(2 + 0)}{(2x - 1)^{2}})x - \frac{2}{(2x - 1)} + 3(\frac{-(2 + 0)}{(2x - 1)^{2}}))}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}})}{(2x + 1)}\\=& - \frac{4x{\frac{1}{2}}^{(\frac{3}{2}x)}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x - 1)^{2}} + \frac{2 * {\frac{1}{2}}^{(\frac{3}{2}x)}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x - 1)} + \frac{6 * {\frac{1}{2}}^{(\frac{3}{2}x)}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x - 1)^{2}} + \frac{3 * {\frac{1}{2}}^{(\frac{3}{2}x)}ln(\frac{1}{2})}{2({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{4x}{(2x + 1)^{2}({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} + \frac{8x^{2}}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x + 1)(2x - 1)^{2}} - \frac{4x}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x + 1)(2x - 1)} - \frac{16x}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x + 1)(2x - 1)^{2}} + \frac{6}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x + 1)(2x - 1)^{2}} + \frac{2}{({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})^{2}(2x + 1)(2x - 1)} - \frac{2}{(2x + 1)^{2}({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})} - \frac{2}{(2x + 1)({\frac{1}{2}}^{(\frac{3}{(2n - 2)})} - \frac{2x}{(2x - 1)} + \frac{3}{(2x - 1)})}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!