TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}^+ \cr \cr f(x)&=&\ln\left(\dfrac{1}{x}\right) \cr\cr \quad g(h(x)) &=& \ln(h(x)) & \Rightarrow & g'(x) &=& \dfrac{1}{h(x)} \cr \quad h(x) &=& \dfrac{1}{x} = x^{-1} & \Rightarrow & h'(x) &=& -1x^{-2} = -\dfrac{1}{x^2} \cr\cr f'(x) &=& \genfrac{}{}{1pt}{0}{1}{\dfrac{1}{x}} \cdot \left(-\dfrac{1}{x^2} \right) \cr\cr &=& -x \cdot \dfrac{1}{x^2} \cr\cr &=&-\dfrac{1}{x}\end{array}