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Beliebt Rechnen >

derivative h(x)=ln(x+sqrt(x^2-6))

Lösung

ableitung von

h (x) = ln (x + x^{2} - 6)

Lösung

\frac{1}{x ^{2} - 6}

Schritte zur Lösung

\frac{d}{d x} (ln (x + x^{2} - 6))

Wende die Kettenregel an:

\frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

= \frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

\frac{d}{d x} (x + x^{2} - 6) = 1 + \frac{x}{x ^{2} - 6}

= \frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6})

Vereinfache

\frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6}) : \frac{1}{x ^{2} - 6}

= \frac{1}{x ^{2} - 6}

Graph

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