derivative of \sqrt[5]{(x^2+x/(x+1)})

Lösung

\frac{d}{d x} (5 \frac{x ^{2} + x}{x + 1})

\frac{1}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 \frac{x ^{2} + x}{x + 1})

Wende die Kettenregel an:

\frac{1}{5 ( \frac{x ^{2} + x}{x + 1} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{x ^{2} + x}{x + 1})

= \frac{1}{5 ( \frac{x ^{2} + x}{x + 1} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{x ^{2} + x}{x + 1})

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

= \frac{1}{5 ( \frac{x ^{2} + x}{x + 1} ) ^{\frac{4}{5}}} \cdot 1

Vereinfache

\frac{1}{5 ( \frac{x ^{2} + x}{x + 1} ) ^{\frac{4}{5}}} \cdot 1 : \frac{1}{5 x ^{\frac{4}{5}}}

= \frac{1}{5 x ^{\frac{4}{5}}}

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