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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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