(\partial)/(\partial y)((p(y,x))(x-y))

解

\frac{\partial}{\partial y} ((p (y, x)) (x - y))

p ((, x \cdot 1) (x - y) + (- 1) (y, x))

解答ステップ

\frac{\partial}{\partial y} ((p (y, x)) (x - y))

p, x

を定数として扱う

定数を除去:

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

= p \frac{\partial}{\partial y} ((y, x) (x - y))

積の法則を適用:

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

f = y, x, g = x - y

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

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

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

= p ((, x \cdot 1) (x - y) + (- 1) (y, x))