(\partial)/(\partial x)(arctan(9x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial 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}

d er i v a t i v e y = (4 x^{2} + 3) (2 x - 3)

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