derivative of | 1/x |

Lösung

\frac{d}{d x} (\frac{1}{x})

- \frac{∣ x ∣}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x})

Wende die Kettenregel an:

\frac{\frac{1}{x}}{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

= \frac{\frac{1}{x}}{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

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

= \frac{\frac{1}{x}}{\frac{1}{x}} (- \frac{1}{x ^{2}})

Vereinfache

\frac{\frac{1}{x}}{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{∣ x ∣}{x ^{3}}

= - \frac{∣ x ∣}{x ^{3}}