TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+_0 \\\\f(x) &=& \sqrt{e^{\sqrt{x}-t}} \\&=& \left(e^{\sqrt{x}-t}\right)^{\frac{1}{2}} \\\\\quad g(h(k(x))) &=& \left(h\left(k(x)\right)\right)^{\frac{1}{2}} & \Rightarrow & g'(h(k(x))) &=& \dfrac{1}{2}\left(h\left(k(x)\right)\right)^{-\frac{1}{2}} \\\quad h(k(x)) &=& e^{k(x)} & \Rightarrow & h'(k(x)) &=& e^{k(x)} \\\quad k(x) &=& \sqrt{x}-t & \Rightarrow & k'(x) &=& \dfrac{1}{2\sqrt{x}} \\\\f'(x) &=& \dfrac{1}{2}\left(e^{\sqrt{x}-t}\right)^{-\frac{1}{2}} \cdot e^{\sqrt{x}-t}\cdot\dfrac{1}{2\sqrt{x}} \\\\&=& \dfrac{1}{4}\cdot\dfrac{e^{\sqrt{x}-t}}{\sqrt{e^{\sqrt{x}-t}}}\cdot\dfrac{1}{\sqrt{x}} \\\\&=& \dfrac{\sqrt{e^{\sqrt{x}-t}}}{4\sqrt{x}}\end{array}