d/(d{x)}(({z})({x}^2+{y}^2-2{z}^2+12{x}-8{z}-4))

解

\frac{d}{d x} ((z) (x^{2} + y^{2} - 2 z^{2} + 12 x - 8 z - 4))

z (2 x + 12)

解答ステップ

\frac{d}{d x} ((z) (x^{2} + y^{2} - 2 z^{2} + 12 x - 8 z - 4))

定数を除去:

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

= z \frac{d}{d x} (x^{2} + y^{2} - 2 z^{2} + 12 x - 8 z - 4)

和/差の法則を適用:

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

= z (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) - \frac{d}{d x} (2 z^{2}) + \frac{d}{d x} (12 x) - \frac{d}{d x} (8 z) - \frac{d}{d x} (4))

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

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

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

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (8 z) = 0

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

= z (2 x + 0 - 0 + 12 - 0 - 0)

簡素化

= z (2 x + 12)