Aufgabe:
Nach x_1 ableiten$$f(x_{1},x_{2},x_{3})= \sqrt{x_{1}x_{2}x_{3}} $$
Problem/Ansatz:
$$\frac{d}{dx_{1}}f(x_{1},x_{2},x_{3})= \frac{1}{2}(x_{1}x_{2}x_{3})^{-\frac{1}{2}}\cdot\frac{d}{dx_{1}}[x_{1}x_{2}x_{3}] \\ = \frac{1}{2}(x_{1}x_{2}x_{3})^{-\frac{1}{2}}\cdot x_{2}x_{3} \\ = \frac{1}{2}(x_{1})^{-\frac{1}{2}}\cdot(x_{2}x_{3})^{\frac{1}{2}} \\ = \frac{ \sqrt{ x_{ 2 }x_{ 3 } }\cdot\sqrt{ x_{ 1 } } } { 2\sqrt{ x_{ 1}\cdot\sqrt{ x_{1 }}}} \\ = \frac{\sqrt{x_{1}x_{2}x_{3}}}{2 x_{1}}$$
