TeX Quellcode:

\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+ \\\\f(x) &=& \dfrac{15}{x^2}\ln(x)+125 \\\\\quad u(x) &=& \dfrac{15}{x^2} = 15x^{-2} &\Rightarrow &u'(x) &=& 15\cdot(-2)x^{-3} = -\dfrac{30}{x^3} \\\quad v(x) &=& \ln(x) &\Rightarrow &v'(x) &=& \dfrac{1}{x} \\\\f'(x) &=& -\dfrac{30}{x^3}\ln(x)+\dfrac{15}{x^2}\cdot \dfrac{1}{x} \\\\&=& \dfrac{15-30\ln(x)}{x^3}\end{array}