TeX Quellcode:

\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+_0 \\\\g(x) &=& 2^x\sqrt[10]{1024x} \\&=& 2^x\cdot 2\sqrt[10]{x} \\\\\quad u(x) &=& 2^x &\Rightarrow & u'(x)&=& 2^x\cdot\ln(2) \\\quad v(x) &=& 2\sqrt[10]{x} = 2x^{\frac{1}{10}} &\Rightarrow & v'(x) &=& 2\cdot\dfrac{1}{10}x^{-\frac{9}{10}} = \dfrac{1}{5\sqrt[10]{x^9}} \\\\f'(x) &=& 2^x\cdot\ln(2)\cdot 2\sqrt[10]{x}+2^x\cdot \dfrac{1}{5}\cdot\dfrac{1}{\sqrt[10]{x^9}} \\\\&=& 2^{x+1}\cdot\ln(2)\sqrt[10]{x}+2^{x+1}\cdot\dfrac{1}{10\sqrt[10]{x^9}} \\\\&=& 2^{x+1}\left(\dfrac{1}{10\sqrt[10]{x^9}}+\ln(2)\sqrt[10]{x}\right)\end{array}