TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{-5\right\}}\cr \cr f(x) &=& \dfrac{x^{3}}{x + 5}\cr \cr \quad u(x) &=& x^{3} & \Rightarrow & u'(x) &=&3 x^{2}\cr \quad v(x) &=&x + 5 & \Rightarrow & v'(x) &=& 1 \cr \cr f'(x) &=& \dfrac{3 x^{2}\cdot \left(x + 5\right)-x^{3} \cdot 1}{\left(x + 5\right)^2}\cr \cr &=& \dfrac{3x^{3} + 15x^2-x^{3}}{\left(x + 5\right)^{2}}\cr \cr &=& \dfrac{x^{2} \left(2 x + 15\right)}{\left(x + 5\right)^{2}}\end{array}