TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\{x\in\mathbb{R}\vert x\neq\pm 1\} \cr \cr f(x) &=& \dfrac{2}{2x^2-2} \cr\cr &=& 2(2x^2-2)^{-1} \cr\cr \quad g(h(x)) &=& 2(h(x))^{-1} & \Rightarrow & g'(h(x)) &=& -2(h(x))^{-2} = \dfrac{-2}{h(x)^2} \cr \quad h(x) &=& 2x^2-2 & \Rightarrow & h'(x) &=& 4x \cr\cr f'(x) &=& \dfrac{-2}{\left( 2x^2-2 \right)^2} \cdot 4x \cr\cr &=& \dfrac{-8x}{4x^4-8x^2+4} \cr\cr &=& \dfrac{-2x}{x^4-2x^2+1} \cr\cr &=& -\dfrac{2x}{(x^2-1)^2} \end{array}