derivative of 1/(|x|)

Lösung

\frac{d}{d x} (\frac{1}{∣ x ∣})

- \frac{1}{x ∣ x ∣}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{∣ x ∣})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (∣ x ∣^{- 1})

Wende die Kettenregel an:

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

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

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

= - \frac{1}{∣ x ∣ ^{2}} \cdot \frac{x}{∣ x ∣}

Vereinfache

- \frac{1}{∣ x ∣ ^{2}} \cdot \frac{x}{∣ x ∣} : - \frac{1}{x ∣ x ∣}

= - \frac{1}{x ∣ x ∣}

\int x sin (\frac{x}{3}) d x

\int - ln (x + 1) d x

\frac{d}{d x} (\frac{b}{cos ( θ )})

\int + 17 cot^{4} (x) d x

\frac{3 d y}{d x} + 15 y = 90, y (0) = 0