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Beliebt Rechnen >

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

Lösung

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

Lösung

\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}

Graph

Beliebte Beispiele

limit as x approaches-1 of x/((x+1)^2)

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

derivative of 2sqrt(x+8)

\frac{d}{d x} (2 x + 8)

derivative e^{4x}*4

d er i v a t i v e e^{4 x} \cdot 4

derivative pi^x

d er i v a t i v e π^{x}

sum from n=0 to infinity of 2+4+6+8

n = 0 \sum \infty 2 + 4 + 6 + 8