TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{0\right\}}\cr \cr f(y) &=& \dfrac{\pi \sin{\left(y \right)}}{- y^{2}} -12\pi\cr \cr \quad u(y) &=& \pi \sin{\left(y \right)} & \Rightarrow & u'(y) &=&\pi \cos{\left(y \right)}\cr \quad v(y) &=&- y^{2} & \Rightarrow & v'(y) &=& - 2 y\cr \cr f'(y) &=& \dfrac{\pi \cos{\left(y \right)}\cdot \left(- y^{2}\right)-\pi \sin{\left(y \right)} \cdot \left(- 2 y\right)}{\left(- y^{2}\right)^2}\cr \cr &=& \dfrac{- \pi y^{2} \cos{\left(y \right)}+2 \pi y \sin{\left(y \right)}}{y^{4}}\cr \cr &=& \dfrac{\pi y \left(- y \cos{\left(y \right)} + 2 \sin{\left(y \right)}\right)}{y^{4}}\cr \cr &=& \dfrac{\pi \left(- y \cos{\left(y \right)} + 2 \sin{\left(y \right)}\right)}{y^{3}}\end{array}