(\partial)/(\partial y)(({g}(y,x))(x+y))

解

\frac{\partial}{\partial y} ((g (y, x)) (x + y))

\frac{\partial}{\partial y} (g (y, x)) (x + y) + 1 \cdot g (y, x)

解答ステップ

\frac{\partial}{\partial y} ((g (y, x)) (x + y))

x

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 (y, x), g = x + y

= \frac{\partial}{\partial y} (g (y, x)) (x + y) + \frac{\partial}{\partial y} (x + y) g (y, x)

\frac{\partial}{\partial y} (x + y) = 1

= \frac{\partial}{\partial y} (g (y, x)) (x + y) + 1 \cdot g (y, x)