(\partial)/(\partial r)(arctan(rs))

Lösung

\frac{\partial}{\partial r} (arctan (rs))

\frac{s}{r ^{2} s ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial r} (arctan (rs))

Behandle

s

als Konstante

Wende die Kettenregel an:

\frac{1}{( rs ) ^{2} + 1} \frac{\partial}{\partial r} (rs)

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

\frac{\partial}{\partial r} (rs) = s

= \frac{1}{( rs ) ^{2} + 1} s

Vereinfache

\frac{1}{( rs ) ^{2} + 1} s : \frac{s}{r ^{2} s ^{2} + 1}

= \frac{s}{r ^{2} s ^{2} + 1}

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