TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+ \\\\f(x) &=& \ln\left(\dfrac{12}{7}\cdot \dfrac{1}{\sqrt{x}}\right) \\\\&=& \ln\left(\dfrac{12}{7}x^{-\frac{1}{2}}\right) \\\\\quad g(h(x)) &=& \ln\left(h(x)\right) & \Rightarrow & g'(h(x)) &=& \dfrac{1}{h(x)} \\\\\quad h(x) &=& \dfrac{12}{7}x^{-\frac{1}{2}} & \Rightarrow & h'(x) &=& \dfrac{12}{7}\cdot \left(-\dfrac{1}{2}\right)x^{-\frac{3}{2}} = -\dfrac{6}{7}\cdot x^{-\frac{3}{2}} \\\\f'(x) &=& \dfrac{1}{\dfrac{12}{7}x^{-\frac{1}{2}}} \cdot \left(-\dfrac{6}{7}x^{-\frac{3}{2}}\right) \\\\&=& \dfrac{7}{12}x^{\frac{1}{2}} \cdot \left(-\dfrac{6}{7}\right) x^{-\frac{3}{2}} \\\\&=& -\dfrac{1}{2}x^{-1} \\\\&=& -\dfrac{1}{2x}\end{array}