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Beliebt Rechnen >

derivative of arcsinh((2x+5/(sqrt(23))))

Lösung

\frac{d}{d x} (arcsinh (\frac{2 x + 5}{23}))

Lösung

\frac{1}{x ^{2} + 5 x + 12}

Schritte zur Lösung

\frac{d}{d x} (arcsinh (\frac{2 x + 5}{23}))

Wende die Kettenregel an:

\frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \frac{d}{d x} (\frac{2 x + 5}{23})

= \frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \frac{d}{d x} (\frac{2 x + 5}{23})

\frac{d}{d x} (\frac{2 x + 5}{23}) = \frac{2}{23}

= \frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \cdot \frac{2}{23}

Vereinfache

\frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \cdot \frac{2}{23} : \frac{1}{x ^{2} + 5 x + 12}

= \frac{1}{x ^{2} + 5 x + 12}

Graph

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