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

解

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

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

解答ステップ

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

s

を定数として扱う

連鎖法則を適用:

\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

簡素化

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

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