TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{0; 1\right\}} \cr \cr g(x) &=& \dfrac{- 2 \ln{\left(x \right)}}{x^{31} - x^{26}} \cr \cr \quad u(x) &=& - 2 \ln{\left(x \right)} & \Rightarrow & u'(x) &=&- \dfrac{2}{x}\cr \quad v(x) &=&x^{31} - x^{26} & \Rightarrow & v'(x) &=& 31 x^{30} - 26 x^{25} \cr \cr g'(x) &=& \dfrac{- \dfrac{2}{x}\cdot \left(x^{31} - x^{26}\right)-\left(- 2 \ln{\left(x \right)} \right)\cdot \left(31 x^{30} - 26 x^{25}\right)}{\left(x^{31} - x^{26}\right)^2} \cr \cr &=& \dfrac{-2 x^{30} +2x^{25} +62 x^{30}\ln{\left(x \right)}-52x^{25}\ln\left(x\right)}{\left(x^{31} - x^{26}\right)^{2}} \cr\cr &=& \dfrac{2 x^{25} \left(- x^{5} + 1 + 31 x^{5} \ln\left(x\right) - 26 \ln{\left(x \right)}\right)}{x^{52}\left(x^{5} - 1\right)^{2}} \cr\cr &=& \dfrac{2 \left(- x^{5} + \left(31 x^{5} - 26\right) \ln{\left(x \right)} + 1\right)}{x^{27}\left(x^{5} - 1\right)^{2}}\end{array}