(\partial)/(\partial x)((w(x,y))(x^2+y^2))

解答

\frac{\partial}{\partial x} ((w (x, y)) (x^{2} + y^{2}))

w ((, y \cdot 1) (x^{2} + y^{2}) + 2 x (x, y))

求解步骤

\frac{\partial}{\partial x} ((w (x, y)) (x^{2} + y^{2}))

将

w, y

视为常数

将常数提出:

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

= w \frac{\partial}{\partial x} ((x, y) (x^{2} + y^{2}))

使用微分乘法定则:

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

f = x, y, g = x^{2} + y^{2}

= w (\frac{\partial}{\partial x} (x, y) (x^{2} + y^{2}) + \frac{\partial}{\partial x} (x^{2} + y^{2}) (x, y))

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

\frac{\partial}{\partial x} (x^{2} + y^{2}) = 2 x

= w ((, y \cdot 1) (x^{2} + y^{2}) + 2 x (x, y))

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