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Beliebt Rechnen >

derivative of ln(x+sqrt(x^2+3))

Lösung

\frac{d}{d x} (ln (x + x^{2} + 3))

Lösung

\frac{1}{x ^{2} + 3}

Schritte zur Lösung

\frac{d}{d x} (ln (x + x^{2} + 3))

Wende die Kettenregel an:

\frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

= \frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

\frac{d}{d x} (x + x^{2} + 3) = 1 + \frac{x}{x ^{2} + 3}

= \frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3})

Vereinfache

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

= \frac{1}{x ^{2} + 3}

Graph

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2x(1+y)dx-ydy=0

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