There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(\frac{(90 - 3x)}{(3 - \frac{49}{x})} + \frac{(180 - 7x)}{(\frac{49}{x} - 2)})}{(\frac{49}{x})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{\frac{3}{49}x^{2}}{(\frac{-49}{x} + 3)} - \frac{\frac{1}{7}x^{2}}{(\frac{49}{x} - 2)} + \frac{\frac{180}{49}x}{(\frac{49}{x} - 2)} + \frac{\frac{90}{49}x}{(\frac{-49}{x} + 3)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - \frac{\frac{3}{49}x^{2}}{(\frac{-49}{x} + 3)} - \frac{\frac{1}{7}x^{2}}{(\frac{49}{x} - 2)} + \frac{\frac{180}{49}x}{(\frac{49}{x} - 2)} + \frac{\frac{90}{49}x}{(\frac{-49}{x} + 3)}\right)}{dx}\\=& - \frac{3}{49}(\frac{-(\frac{-49*-1}{x^{2}} + 0)}{(\frac{-49}{x} + 3)^{2}})x^{2} - \frac{\frac{3}{49}*2x}{(\frac{-49}{x} + 3)} - \frac{1}{7}(\frac{-(\frac{49*-1}{x^{2}} + 0)}{(\frac{49}{x} - 2)^{2}})x^{2} - \frac{\frac{1}{7}*2x}{(\frac{49}{x} - 2)} + \frac{180}{49}(\frac{-(\frac{49*-1}{x^{2}} + 0)}{(\frac{49}{x} - 2)^{2}})x + \frac{\frac{180}{49}}{(\frac{49}{x} - 2)} + \frac{90}{49}(\frac{-(\frac{-49*-1}{x^{2}} + 0)}{(\frac{-49}{x} + 3)^{2}})x + \frac{\frac{90}{49}}{(\frac{-49}{x} + 3)}\\=&\frac{180}{(\frac{49}{x} - 2)^{2}x} - \frac{6x}{49(\frac{-49}{x} + 3)} - \frac{90}{(\frac{-49}{x} + 3)^{2}x} - \frac{2x}{7(\frac{49}{x} - 2)} + \frac{3}{(\frac{-49}{x} + 3)^{2}} - \frac{7}{(\frac{49}{x} - 2)^{2}} + \frac{180}{49(\frac{49}{x} - 2)} + \frac{90}{49(\frac{-49}{x} + 3)}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!