There are 1 questions in this calculation: for each question, the 2 derivative of a is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (-(\frac{aa}{(b)})t(a - 1)e^{-(\frac{t}{b})a}){\frac{1}{(1 - e^{-(\frac{t}{b})a})}}^{2}\ with\ respect\ to\ a:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-ta^{3}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{ta^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{-ta^{3}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{ta^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b}\right)}{da}\\=&\frac{-(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})ta^{3}e^{\frac{-ta}{b}}}{b} - \frac{t*3a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} - \frac{ta^{3}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}bb} + \frac{(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})ta^{2}e^{\frac{-ta}{b}}}{b} + \frac{t*2ae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{ta^{2}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}bb}\\=&\frac{2t^{2}a^{3}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} - \frac{3ta^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{t^{2}a^{3}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} - \frac{2t^{2}a^{2}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} + \frac{2tae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} - \frac{t^{2}a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2t^{2}a^{3}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} - \frac{3ta^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{t^{2}a^{3}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} - \frac{2t^{2}a^{2}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} + \frac{2tae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} - \frac{t^{2}a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}}\right)}{da}\\=&\frac{2(\frac{-3(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{4}})t^{2}a^{3}e^{{\frac{-ta}{b}}*{2}}}{b^{2}} + \frac{2t^{2}*3a^{2}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} + \frac{2t^{2}a^{3}*2e^{\frac{-ta}{b}}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}b} - \frac{3(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})ta^{2}e^{\frac{-ta}{b}}}{b} - \frac{3t*2ae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} - \frac{3ta^{2}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}bb} + \frac{(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})t^{2}a^{3}e^{\frac{-ta}{b}}}{b^{2}} + \frac{t^{2}*3a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} + \frac{t^{2}a^{3}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}b} - \frac{2(\frac{-3(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{4}})t^{2}a^{2}e^{{\frac{-ta}{b}}*{2}}}{b^{2}} - \frac{2t^{2}*2ae^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} - \frac{2t^{2}a^{2}*2e^{\frac{-ta}{b}}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}b} + \frac{2(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})tae^{\frac{-ta}{b}}}{b} + \frac{2te^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{2tae^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}bb} - \frac{(\frac{-2(\frac{-e^{\frac{-ta}{b}}*-t}{b} + 0)}{(-e^{\frac{-ta}{b}} + 1)^{3}})t^{2}a^{2}e^{\frac{-ta}{b}}}{b^{2}} - \frac{t^{2}*2ae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} - \frac{t^{2}a^{2}e^{\frac{-ta}{b}}*-t}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}b}\\=&\frac{-6t^{3}a^{3}e^{{\frac{-ta}{b}}*{3}}}{(-e^{\frac{-ta}{b}} + 1)^{4}b^{3}} + \frac{12t^{2}a^{2}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} - \frac{6t^{3}a^{3}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{3}} - \frac{6tae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} + \frac{6t^{2}a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} - \frac{t^{3}a^{3}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{3}} + \frac{6t^{3}a^{2}e^{{\frac{-ta}{b}}*{3}}}{(-e^{\frac{-ta}{b}} + 1)^{4}b^{3}} - \frac{8t^{2}ae^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{2}} + \frac{6t^{3}a^{2}e^{{\frac{-ta}{b}}*{2}}}{(-e^{\frac{-ta}{b}} + 1)^{3}b^{3}} + \frac{2te^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b} - \frac{4t^{2}ae^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{2}} + \frac{t^{3}a^{2}e^{\frac{-ta}{b}}}{(-e^{\frac{-ta}{b}} + 1)^{2}b^{3}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!