TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}\setminus_{\left\{- \frac{1}{7}\right\}}\cr \cr f(x) &=& \dfrac{21 e^{x}}{7 x + 1}\cr \cr \quad u(x) &=& 21 e^{x} & \Rightarrow & u'(x) &=&21 e^{x}\cr \quad v(x) &=&7 x + 1 & \Rightarrow & v'(x) &=& 7\cr \cr f'(x) &=& \dfrac{21 e^{x}\cdot \left(7 x + 1\right)-21 e^{x}\cdot 7}{\left(7 x + 1\right)^2}\cr \cr &=& \dfrac{147x e^x + 21 e^{x}-147 e^{x}}{\left(7 x + 1\right)^{2}}\cr \cr &=& \dfrac{\left(147 x - 126\right) e^{x}}{\left(7 x + 1\right)^{2}}\end{array}