TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{0\right\}}\cr \cr f(x) &=& \dfrac{\ln{\left(x \right)}}{x^{11}} \cr \cr \quad u(x) &=& \ln{\left(x \right)} & \Rightarrow & u'(x) &=&\dfrac{1}{x}\cr \quad v(x) &=&x^{11} & \Rightarrow & v'(x) &=& 11 x^{10}\cr \cr f'(x) &=& \dfrac{\dfrac{1}{x}\cdot x^{11}-\ln{\left(x \right)} \cdot 11 x^{10}}{\left(x^{11}\right)^2}\cr \cr &=& \dfrac{x^{10}-11 x^{10} \ln{\left(x \right)}}{x^{22}}\cr \cr &=& \dfrac{x^{10} \left(1 - 11 \ln{\left(x \right)}\right)}{x^{22}} \cr \cr &=& \dfrac{1 - 11 \ln{\left(x \right)}}{x^{12}}\end{array}