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

解

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

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

解答ステップ

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

r

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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