Hallo,

\( \frac {C'(x) \cdot \sqrt{1+2x} - \frac {C(x)} {\sqrt{1+2x}}} {1 +2x} + \frac {\frac {C(x)} {\sqrt{1+2x}}} {1 +2x} \\ = \frac{C'(x) \cdot \sqrt{1+2x}} {1+2x} - \frac {\frac {C(x)} {\sqrt{1+2x}}} {1 +2x} + \frac {\frac {C(x)} {\sqrt{1+2x}}} {1 +2x} \\ = \frac{C'(x) \cdot \sqrt{1+2x}} {1+2x} \)

Nun gilt

\( \frac {\sqrt{x}} x = x^{0{,}5} \cdot x^{-1} = x^{0{,}5-1} = x^{-0{,}5} = \frac 1 {\sqrt{x}} \)

Also erhalten wir

\(  \frac{C'(x) \cdot \sqrt{1+2x}} {1+2x} = \frac {C'(x)} { \sqrt{1+2x}} \)

Grüße Christian