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Beliebt Rechnen >

derivative of arctan(x-1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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