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