(\partial)/(\partial {g)}(2pisqrt(l/({g))})

解

\frac{\partial}{\partial g} (2 π \frac{l}{g})

- \frac{π l}{g ^{\frac{3}{2}}}

解答ステップ

\frac{\partial}{\partial g} (2 π \frac{l}{g})

定数を除去:

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

= 2 π \frac{\partial}{\partial g} (\frac{l}{g})

連鎖法則を適用:

\frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial g} (\frac{l}{g})

= \frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial g} (\frac{l}{g})

\frac{\partial}{\partial g} (\frac{l}{g}) = - \frac{l}{g ^{2}}

= 2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}})

簡素化

2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}}) : - \frac{π l}{g ^{\frac{3}{2}}}

= - \frac{π l}{g ^{\frac{3}{2}}}