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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e ln (sin (x))

y^{^{'}} = y x^{2}

l a pl a ce t r an s f or m t^{3} cos (3 t)

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