TeX Quellcode:

\begin{array}{ccllrcl}\quad\mathbb{D} &=& \mathbb{R}\\\\f(x) &=& \left(x-1\right)\cdot\left(\dfrac{47}{2}x^2+16x+7\right)\\\\\quad u(x) &=& x-1 &\Rightarrow & u'(x) &=& 1\\\quad v(x) &=& \dfrac{47}{2}x^2+16x+7 &\Rightarrow & v'(x) &=& 47x+16\\\\f'(x) &=& 1\cdot \left(\dfrac{47}{2}x^2+16x+7\right)+\left(x-1\right)\cdot\left(47x+16\right)\\\\&=& \dfrac{47}{2}x^2+16x+7+47x^2+16x-47x-16\\\\&=& \dfrac{141}{2}x^2-15x-9\end{array}