(\partial)/(\partial x)(1/(|x-a|))

Lösung

\frac{\partial}{\partial x} (\frac{1}{∣ x - a ∣})

- \frac{1}{∣ x - a ∣ ( x - a )}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{∣ x - a ∣})

Wende Exponentenregel an:

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

= \frac{\partial}{\partial x} (∣ x - a ∣^{- 1})

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (∣ x - a ∣) = \frac{x - a}{∣ x - a ∣}

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

Vereinfache

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

= - \frac{1}{∣ x - a ∣ ( x - a )}

a re a x = y^{2} - 6 y, x = 5 y - y^{2}

\int \frac{- 1}{y ^{2}} d y

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