TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R}^+\setminus_{\left\{1\right\}} \cr \cr f(x) &=& \dfrac{x^{2} + 18}{18 \lg\left(x \right)} \cr \cr \quad u(x) &=& x^{2} + 18 & \Rightarrow & u'(x) &=&2 x\cr \quad v(x) &=&18 \lg\left(x \right) & \Rightarrow & v'(x) &=& \dfrac{18}{x \ln{\left(10 \right)}}\cr \cr f'(x) &=& \dfrac{2 x\cdot 18 \lg\left(x \right)-\left(x^{2} + 18 \right)\cdot \dfrac{18}{x \ln{\left(10 \right)}}}{\left(18 \lg\left(x \right)\right)^2} \cr \cr &=& \dfrac{36 x \lg{\left(x \right)}-\dfrac{18x^{2} + 324}{x \ln{\left(10 \right)}}}{324 \lg^2{\left(x \right)}} \cr\cr &=& \dfrac{\dfrac{36 x^2 \ln(10)\lg{\left(x \right)}}{x \ln(10)}-\dfrac{18x^{2} + 324}{x \ln{\left(10 \right)}}}{324 \lg^2{\left(x \right)}} \cr\cr &=& \dfrac{18 \left(2 x^{2} \ln(10)\lg{\left(x \right)} - x^{2} - 18\right)}{x \ln{\left(10 \right)}}\cdot\dfrac{1}{324 \lg^2{\left(x \right)}} \cr \cr &=& \dfrac{2 x^{2} \ln(10)\lg{\left(x \right)} - x^{2} - 18}{18 x \ln(10) \lg^2{\left(x \right)}}\end{array}