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