TeX Quellcode:
\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+_0 \\\\f(x) &=& \left(4x^2-16\right)\sqrt{23x}-5 \\\\\quad u(x) &=& 4x^2-16 &\Rightarrow & u'(x) &=& 8x \\\quad v(x) &=& \sqrt{23x} = \sqrt{23}\sqrt{x} &\Rightarrow & v'(x) &=& \sqrt{23}\dfrac{1}{2\sqrt{x}} = \dfrac{\sqrt{23}}{2\sqrt{x}} \\\\f'(x) &=& 8x\cdot \sqrt{23x}+\left(4x^2-16\right)\cdot \dfrac{\sqrt{23}}{2\sqrt{x}} \\\\&=& 8x\sqrt{23x}+\dfrac{2x^2\sqrt{23}}{\sqrt{x}}-\dfrac{8\sqrt{23}}{\sqrt{x}}\end{array}