TeX Quellcode:

\begin{array}{ccllrcl}\quad\mathbb{D} &=& \mathbb{R}\\\\f(x) &=& \left(\dfrac{1}{8}x^3+5x\right)\cdot\sqrt{8}x\\\\\quad u(x) &=& \dfrac{1}{8}x^3+5x &\Rightarrow & u'(x) &=& \dfrac{3}{8}x^{2}+5\\\quad v(x) &=& \sqrt{8}x &\Rightarrow & v'(x) &=& \sqrt{8}\\\\f'(x) &=& \left(\dfrac{3}{8}x^{2}+5\right)\cdot\sqrt{8}x+\left(\dfrac{1}{8}x^3+5x\right)\cdot\sqrt{8}\\\\&=& \sqrt{8}\left(\dfrac{3}{8}x^{3}+5x+\dfrac{1}{8}x^3+5x\right)\\\\&=& \sqrt{8}\left(\dfrac{1}{2}x^{3}+10x\right)\\\end{array}