TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D} &=& \left]-\frac{1}{756};0\right[ \\\\f(x) &=& \ln\left(-42x^4-\dfrac{1}{18}x^3\right) \\\\\quad g(h(x)) &=& \ln\left(h(x)\right) & \Rightarrow & g'(h(x)) &=& \dfrac{1}{h(x)} \\\quad h(x) &=& -42x^4-\dfrac{1}{18}x^3 & \Rightarrow & h'(x) &=& -168x^3-\dfrac{1}{6}x^2 \\\\f'(x) &=& \dfrac{1}{-42x^4-\frac{1}{18}x^3}\cdot \left(-168x^3-\dfrac{1}{6}x^2\right) \\\\&=& \dfrac{-168x^3-\frac{1}{6}x^2}{-42x^4-\frac{1}{18}x^3} \\\\&=& \dfrac{x^2\left(-168x-\frac{1}{6}\right)}{x^2\left(-42x^2-\frac{1}{18}x\right)} \\\\&=& \dfrac{-168x-\frac{1}{6}}{-42x^2-\frac{1}{18}x}\end{array}