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Beliebt Rechnen >

(\partial)/(\partial x)(arctan(2x))

Lösung

\frac{\partial}{\partial x} (arctan (2 x))

Lösung

\frac{2}{4 x ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (arctan (2 x))

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

Vereinfache

\frac{1}{( 2 x ) ^{2} + 1} \cdot 2 : \frac{2}{4 x ^{2} + 1}

= \frac{2}{4 x ^{2} + 1}

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