TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R}\setminus_{\{0; 1\}} \\\\f(x) &=& \dfrac{-63}{x^2-\frac{1}{x}} \\&=& -63\left(x^2-\dfrac{1}{x}\right)^{-1} \\\\\quad g(h(x)) &=& -63\left(h(x)\right)^{-1} & \Rightarrow & g'(h(x)) &=& 63\left(h(x)\right)^{-2} \\\quad h(x) &=& x^2-\dfrac{1}{x} = x^2-x^{-1} & \Rightarrow & h'(x) &=& 2x+x^{-2} = 2x+\dfrac{1}{x^2} \\\\f'(x) &=& 63\left(x^2-\dfrac{1}{x}\right)^{-2}\cdot\left(2x+\dfrac{1}{x^2}\right) \\\\&=& \dfrac{63\cdot\left(2x+\frac{1}{x^2}\right)}{\left(x^2-\frac{1}{x}\right)^{2}} \\\\&=& \dfrac{126x+\frac{63}{x^2}}{\left(x^2-\frac{1}{x}\right)^2}\end{array}