TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R} \\\\f(x) &=& \sqrt[3]{x+4} \\&=& (x+4)^{\frac{1}{3}} \\\\\quad g(h(x)) &=& (h(x))^{\frac{1}{3}} & \Rightarrow & g'(h(x)) &=& \dfrac{1}{3}(h(x))^{-\frac{2}{3}} \\\quad h(x) &=& x+4 & \Rightarrow & h'(x) &=& 1 \\\\f'(x) &=& \dfrac{1}{3}(x+4)^{-\frac{2}{3}}\cdot 1 \\\\&=& \dfrac{1}{3(x+4)^{\frac{2}{3}}} \\\\&=& \dfrac{1}{3\sqrt[3]{(x+4)^2}}\end{array}