(\partial)/(\partial u)(({g}(u,v,w))(uv+w^2))

解

\frac{\partial}{\partial u} ((g (u, v, w)) (uv + w^{2}))

\frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + v g (u, v, w)

解答ステップ

\frac{\partial}{\partial u} ((g (u, v, w)) (uv + w^{2}))

v, w

を定数として扱う

積の法則を適用:

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

f = g (u, v, w), g = uv + w^{2}

= \frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + \frac{\partial}{\partial u} (uv + w^{2}) g (u, v, w)

\frac{\partial}{\partial u} (uv + w^{2}) = v

= \frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + v g (u, v, w)