TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{0\right\}}\cr \cr f(x) &=& \dfrac{\dfrac{x^{2}}{9} + 1}{- 27 x^{13}} \cr \cr \quad u(x) &=& \dfrac{x^{2}}{9} + 1 & \Rightarrow & u'(x) &=&\dfrac{2}{9}x \cr \quad v(x) &=&- 27 x^{13} & \Rightarrow & v'(x) &=& - 351 x^{12}\cr \cr f'(x) &=& \dfrac{\dfrac{2}{9}x\cdot \left(- 27 x^{13}\right)-\left(\dfrac{x^{2}}{9} + 1 \right)\cdot \left(- 351 x^{12}\right)}{\left(- 27 x^{13}\right)^2}\cr \cr &=& \dfrac{- 6 x^{14}+ 39 x^{14} + 351x^{12}}{729 x^{26}}\cr \cr &=& \dfrac{x^{12} \left(33 x^{2} + 351\right)}{729 x^{26}}\cr \cr &=& \dfrac{11 x^{2} + 117}{243 x^{14}}\end{array}