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Beliebt Rechnen >

derivative f(x)=arctan((1+x)/(1-x))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

Graph

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