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

解答

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

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

求解步骤

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

将

p, x

视为常数

将常数提出:

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

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

使用微分乘法定则:

(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))

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