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Beliebt Rechnen >

derivative of ln((x+1/x))

Lösung

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

Lösung

- \frac{1}{x ( x + 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{1}{x ( x + 1 )}

Graph

Beliebte Beispiele

integral of y^2-4

\int y^{2} - 4 d y

integral of cos(x)sin^4(x)

\int cos (x) sin^{4} (x) d x

tangent f(x)= 7/2 x^2-5x+1

t an g e n t f (x) = \frac{7}{2} x^{2} - 5 x + 1

limit as θ approaches 0 of θcot(5θ)

θ \to 0 lim (θ cot (5 θ))

derivative of (x^2-9/(x^2+9))

\frac{d}{d x} (\frac{x ^{2} - 9}{x ^{2} + 9})