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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of (1+sqrt(x)^2)

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

(\partial)/(\partial x)(txe^{(x^2)/(2t)})

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fläche x^4-9x^2,x^2-9

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(\partial)/(\partial x)(1/2 ln(x^2+y^2))

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