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