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Beliebt Rechnen >

derivative of ln((2x+1/(2x-1)))

Lösung

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

Lösung

- \frac{4}{( 2 x + 1 ) ( 2 x - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{2 x + 1}{2 x - 1}) = - \frac{4}{( 2 x - 1 ) ^{2}}

= \frac{1}{\frac{2 x + 1}{2 x - 1}} (- \frac{4}{( 2 x - 1 ) ^{2}})

Vereinfache

\frac{1}{\frac{2 x + 1}{2 x - 1}} (- \frac{4}{( 2 x - 1 ) ^{2}}) : - \frac{4}{( 2 x + 1 ) ( 2 x - 1 )}

= - \frac{4}{( 2 x + 1 ) ( 2 x - 1 )}

Graph

Beliebte Beispiele

limit as x approaches a of 1-sqrt(1-x^2)

x \to a lim (1 - 1 - x^{2})

x y d x + (x + 1) d y = 0

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\frac{d}{d x} (\frac{e ^{x}}{x - 1})

derivative of cos^5(3x)

\frac{d}{d x} (cos^{5} (3 x))

(\partial)/(\partial x)(9)

\frac{\partial}{\partial x} (9)