TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{\sqrt[3]{-32}\right\}}\cr \cr f(x) &=& \dfrac{15 x^{2} - 8 x}{x^{3} + 32}\cr \cr \quad u(x) &=& 15 x^{2} - 8 x & \Rightarrow & u'(x) &=&30 x - 8\cr \quad v(x) &=&x^{3} + 32 & \Rightarrow & v'(x) &=& 3 x^{2}\cr \cr f'(x) &=& \dfrac{\left(30 x - 8\right )\cdot \left(x^{3} + 32\right)-\left(15 x^{2} - 8 x \right)\cdot 3 x^{2}}{\left(x^{3} + 32\right)^2}\cr \cr &=& \dfrac{30x^4-8x^3+960x-256-45x^4+24x^3}{\left(x^{3} + 32\right)^{2}}\cr \cr &=& \dfrac{- 15 x^{4} + 16 x^{3} + 960 x - 256}{\left(x^{3} + 32\right)^{2}}\end{array}