TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R}\setminus_{\{0\}} \\\\f(x) &=& 24\left(x+\dfrac{7}{8x}\right)^2 \\\\\quad g(h(x)) &=& 24\left(h(x)\right)^2 & \Rightarrow & g'(h(x)) &=& 48h(x) \\\quad h(x) &=& x+\dfrac{7}{8x} = x+\dfrac{7}{8}x^{-1} & \Rightarrow & h'(x) &=& 1-\dfrac{7}{8}x^{-2} = 1-\dfrac{7}{8x^2} \\\\f'(x) &=& 48\left(x+\dfrac{7}{8x}\right)\cdot \left(1-\dfrac{7}{8x^2}\right) \\\\&=& 48\left(x-\dfrac{7}{8x}+\dfrac{7}{8x}-\dfrac{49}{64x^3}\right) \\\\&=& 48\left(x-\dfrac{49}{64x^3}\right) \\\\&=& 48x-\dfrac{147}{4x^3}\end{array}