TeX Quellcode:

\begin{array}{ccllrcl}\quad\mathbb{D} &=& \mathbb{R}\\\\f(x) &=& \left(13x^2+\dfrac{7}{5}x-18\right)\left(11x^2-\dfrac{15}{4}x-1\right)\\\\\quad u(x) &=& 13x^2+\dfrac{7}{5}x-18 \Rightarrow u'(x) = 26x+\dfrac{7}{5}\\\\\quad v(x) &=& 11x^2-\dfrac{15}{4}x-1 \Rightarrow v'(x) = 22x-\dfrac{15}{4}\\\\\\f'(x) &=& \left(26x+\dfrac{7}{5}\right)\cdot\left(11x^2-\dfrac{15}{4}x-1\right)+\left(13x^2+\dfrac{7}{5}x-18\right)\cdot\left(22x-\dfrac{15}{4}\right)\\\\&=& 286x^3-\dfrac{195}{2}x^2-26x+\dfrac{77}{5}x^2-\dfrac{21}{4}x-\dfrac{7}{5}+286x^3-\dfrac{195}{4}x^2+\dfrac{154}{5}x^2-\dfrac{21}{4}x-396x+\dfrac{135}{2}\\\\&=& 572x^3-\dfrac{2.001}{20}x^2-\dfrac{865}{2}x+\dfrac{661}{10}\end{array}