TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R} \\\\f(x) &=& 85\ln\left(e^{3x}+x^2\right)-94 \\\\\quad g(h(k(x))) &=& 85\ln(h(k(x)))-94 & \Rightarrow & g'(h(k(x))) &=& 85\cdot \dfrac{1}{h(k(x))} \\\quad h(k(x)) &=& e^{k(x)}+x^2 & \Rightarrow & h'(k(x)) &=& e^{k(x)}+2x \\\quad k(x) &=& 3x & \Rightarrow & r'(x) &=& 3 \\\\f'(x) &=& 85\cdot \dfrac{1}{e^{3x}+x^2}\cdot \left(e^{3x}\cdot 3+2x\right) \\\\&=& \dfrac{85\cdot \left(3e^{3x}+2x\right)}{e^{3x}+x^2} \\\\&=& \dfrac{\left(255e^{3x}+170x\right)}{e^{3x}+x^2}\end{array}