(\partial)/(\partial s)(rln(r^2+s^2))

解

\frac{\partial}{\partial s} (r ln (r^{2} + s^{2}))

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

解答ステップ

\frac{\partial}{\partial s} (r ln (r^{2} + s^{2}))

r

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= r \frac{\partial}{\partial s} (ln (r^{2} + s^{2}))

連鎖法則を適用:

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

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

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

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

簡素化

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

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