(\partial)/(\partial m)((G(m,r)m)/(r^2))

解

\frac{\partial}{\partial m} (\frac{G ( m , r ) m}{r ^{2}})

\frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + 1 \cdot G (m, r))

解答ステップ

\frac{\partial}{\partial m} (\frac{G ( m , r ) m}{r ^{2}})

r

を定数として扱う

定数を除去:

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

= \frac{1}{r ^{2}} \frac{\partial}{\partial m} (G (m, r) m)

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = G (m, r), g = m

= \frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + \frac{\partial}{\partial m} (m) G (m, r))

\frac{\partial}{\partial m} (m) = 1

= \frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + 1 \cdot G (m, r))