There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((2{x}^{2}) + ({x}^{52}))}{(3x + 1372x + {x}^{(13791 - {x}^{182})})({(lg(x))}^{74} + {(ln(x))}^{2074})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x^{2}}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))} + \frac{x^{52}}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{2x^{2}}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))} + \frac{x^{52}}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))}\right)}{dx}\\=&\frac{2(\frac{-(1375 + ({x}^{(-x^{182} + 13791)}((-182x^{181} + 0)ln(x) + \frac{(-x^{182} + 13791)(1)}{(x)})))}{(1375x + {x}^{(-x^{182} + 13791)})^{2}})x^{2}}{(lg^{74}(x) + ln^{2074}(x))} + \frac{2(\frac{-(\frac{74lg^{73}(x)}{ln{10}(x)} + \frac{2074ln^{2073}(x)}{(x)})}{(lg^{74}(x) + ln^{2074}(x))^{2}})x^{2}}{(1375x + {x}^{(-x^{182} + 13791)})} + \frac{2*2x}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))} + \frac{(\frac{-(1375 + ({x}^{(-x^{182} + 13791)}((-182x^{181} + 0)ln(x) + \frac{(-x^{182} + 13791)(1)}{(x)})))}{(1375x + {x}^{(-x^{182} + 13791)})^{2}})x^{52}}{(lg^{74}(x) + ln^{2074}(x))} + \frac{(\frac{-(\frac{74lg^{73}(x)}{ln{10}(x)} + \frac{2074ln^{2073}(x)}{(x)})}{(lg^{74}(x) + ln^{2074}(x))^{2}})x^{52}}{(1375x + {x}^{(-x^{182} + 13791)})} + \frac{52x^{51}}{(1375x + {x}^{(-x^{182} + 13791)})(lg^{74}(x) + ln^{2074}(x))}\\=&\frac{364x^{183}{x}^{(-x^{182} + 13791)}ln(x)}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} + \frac{182x^{233}{x}^{(-x^{182} + 13791)}ln(x)}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} - \frac{27582x{x}^{(-x^{182} + 13791)}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} - \frac{148xlg^{73}(x)}{(lg^{74}(x) + ln^{2074}(x))^{2}(1375x + {x}^{(-x^{182} + 13791)})ln{10}} - \frac{74x^{51}lg^{73}(x)}{(lg^{74}(x) + ln^{2074}(x))^{2}(1375x + {x}^{(-x^{182} + 13791)})ln{10}} - \frac{4148xln^{2073}(x)}{(lg^{74}(x) + ln^{2074}(x))^{2}(1375x + {x}^{(-x^{182} + 13791)})} + \frac{2x^{183}{x}^{(-x^{182} + 13791)}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} + \frac{x^{233}{x}^{(-x^{182} + 13791)}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} - \frac{13791x^{51}{x}^{(-x^{182} + 13791)}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} - \frac{2074x^{51}ln^{2073}(x)}{(lg^{74}(x) + ln^{2074}(x))^{2}(1375x + {x}^{(-x^{182} + 13791)})} + \frac{4x}{(lg^{74}(x) + ln^{2074}(x))(1375x + {x}^{(-x^{182} + 13791)})} - \frac{2750x^{2}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} - \frac{1375x^{52}}{(1375x + {x}^{(-x^{182} + 13791)})^{2}(lg^{74}(x) + ln^{2074}(x))} + \frac{52x^{51}}{(lg^{74}(x) + ln^{2074}(x))(1375x + {x}^{(-x^{182} + 13791)})}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!