derivative arctan(9x)

Lösung

ableitung von

arctan (9 x)

\frac{9}{81 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (9 x))

Wende die Kettenregel an:

\frac{1}{( 9 x ) ^{2} + 1} \frac{d}{d x} (9 x)

= \frac{1}{( 9 x ) ^{2} + 1} \frac{d}{d x} (9 x)

\frac{d}{d x} (9 x) = 9

= \frac{1}{( 9 x ) ^{2} + 1} \cdot 9

Vereinfache

\frac{1}{( 9 x ) ^{2} + 1} \cdot 9 : \frac{9}{81 x ^{2} + 1}

= \frac{9}{81 x ^{2} + 1}

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