(\partial)/(\partial m)(-m{g}(m)sin(a))

解

\frac{\partial}{\partial m} (- m g (m) sin (a))

- sin (a) (g (m) + m \frac{\partial}{\partial m} (g (m)))

解答ステップ

\frac{\partial}{\partial m} (- m g (m) sin (a))

定数を除去:

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

= - sin (a) \frac{\partial}{\partial m} (m g (m))

積の法則を適用:

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

f = m, g = g (m)

= - sin (a) (\frac{\partial}{\partial m} (m) g (m) + \frac{\partial}{\partial m} (g (m)) m)

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

= - sin (a) (1 \cdot g (m) + \frac{\partial}{\partial m} (g (m)) m)

簡素化

= - sin (a) (g (m) + m \frac{\partial}{\partial m} (g (m)))