TeX Quellcode:

\begin{array}{ccllrcl}\quad\mathbb{D} &=& \mathbb{R}^+ \\\\f(x) &=& 19x^2\cdot\ln(x)\\\\\quad u(x) &=& 19x^2 &\Rightarrow & u'(x) &=& 38x\\\quad v(x) &=& \ln(x) &\Rightarrow & v'(x) &=& \dfrac{1}{x}\\\\f'(x) &=& 38x\cdot\ln(x)+19x^2\cdot\dfrac{1}{x}\\&=& 38x\cdot\ln(x)+19x\\&=& x\left(38\ln(x)+19\right)\\\end{array}