derivative y=sqrt(11x+\sqrt{11x+\sqrt{11x)}}

Lösung

ableitung von

y = 11 x + 11 x + 11 x

\frac{44 x 11 x + 11 x + 22 x + 11}{8 x 11 x + 11 x 11 x + 11 x + 11 x}

Schritte zur Lösung

\frac{d}{d x} (11 x + 11 x + 11 x)

Wende die Kettenregel an:

\frac{1}{2 11 x + 11 x + 11 x} \frac{d}{d x} (11 x + 11 x + 11 x)

= \frac{1}{2 11 x + 11 x + 11 x} \frac{d}{d x} (11 x + 11 x + 11 x)

\frac{d}{d x} (11 x + 11 x + 11 x) = 11 + \frac{22 x + 11}{4 x 11 x + 11 x}

= \frac{1}{2 11 x + 11 x + 11 x} 11 + \frac{22 x + 11}{4 x 11 x + 11 x}

Vereinfache

\frac{1}{2 11 x + 11 x + 11 x} 11 + \frac{22 x + 11}{4 x 11 x + 11 x} : \frac{44 x 11 x + 11 x + 22 x + 11}{8 x 11 x + 11 x 11 x + 11 x + 11 x}

= \frac{44 x 11 x + 11 x + 22 x + 11}{8 x 11 x + 11 x 11 x + 11 x + 11 x}

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