TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{100\right\}} \cr \cr f(x) &=& \dfrac{x^{4}}{100 - x} \cr \cr \quad u(x) &=& x^{4} & \Rightarrow & u'(x) &=&4 x^{3}\cr \quad v(x) &=&100 - x & \Rightarrow & v'(x) &=& -1\cr \cr f'(x) &=& \dfrac{4 x^{3}\cdot \left(100 - x\right)-x^{4} \cdot \left(-1\right)}{\left(100 - x\right)^2} \cr \cr &=& \dfrac{400x^3-4x^4+x^{4}}{\left(100 - x\right)^{2}}\cr \cr &=& \dfrac{x^{3} \left(400 - 3 x\right)}{\left(100 - x\right)^{2}}\end{array}