d/(d{x)}(({z}(x,y))(4-{x}^2-{y}^2))

解答

\frac{d}{d x} ((z (x, y)) (4 - x^{2} - y^{2}))

z (x, y) (0 - 2 x - 0)

求解步骤

\frac{d}{d x} ((z (x, y)) (4 - x^{2} - y^{2}))

将常数提出:

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

= z (x, y) \frac{d}{d x} (4 - x^{2} - y^{2})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (x, y) (\frac{d}{d x} (4) - \frac{d}{d x} (x^{2}) - \frac{d}{d x} (y^{2}))

\frac{d}{d x} (4) = 0

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y^{2}) = 0

= z (x, y) (0 - 2 x - 0)

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