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Beliebt Rechnen >

derivative of 1/(ln(x^2))

Lösung

\frac{d}{d x} (\frac{1}{ln ( x ^{2} )})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{ln ( x ^{2} )})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

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

Vereinfache

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

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

Graph

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