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Beliebt Rechnen >

derivative of ln(1+5/x)

Lösung

\frac{d}{d x} (ln (1 + \frac{5}{x}))

Lösung

- \frac{5}{x ( x + 5 )}

Schritte zur Lösung

\frac{d}{d x} (ln (1 + \frac{5}{x}))

Wende die Kettenregel an:

\frac{1}{1 + \frac{5}{x}} \frac{d}{d x} (1 + \frac{5}{x})

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

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

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

Vereinfache

\frac{1}{1 + \frac{5}{x}} (- \frac{5}{x ^{2}}) : - \frac{5}{x ( x + 5 )}

= - \frac{5}{x ( x + 5 )}

Graph

Beliebte Beispiele

limit as t approaches pi/3 of cos(t)+2

t \to \frac{π}{3} lim (cos (t) + 2)

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

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\frac{d}{d x} (x csc (2 x))