TeX Quellcode:

\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R}\setminus_{\{0\}} \\\\f(y) &=& \dfrac{16}{\frac{4}{3}y^7 e^{-y}}-\dfrac{14}{9} \\&=& 12y^{-7}e^y -\dfrac{14}{9} \\\\\quad u(y) &=& y^{-7} &\Rightarrow & u'(y)&=& -7y^{-8} \\\quad v(y) &=& e^y &\Rightarrow & v'(y) &=& e^y \\\\f'(y) &=& 12\left(-7y^{-8}\cdot e^y+y^{-7}\cdot e^y\right) \\ &=& 12y^{-8}e^y(-7+y) \\&=& \dfrac{12e^y(y-7)}{y^8}\end{array}