d/(d{x)}(({z})({x}^3+{y}^3+{z}^3+6{x}{y}{z}-2))

解

\frac{d}{d x} ((z) (x^{3} + y^{3} + z^{3} + 6 x y z - 2))

z (3 x^{2} + 6 y z)

解答ステップ

\frac{d}{d x} ((z) (x^{3} + y^{3} + z^{3} + 6 x y z - 2))

定数を除去:

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

= z \frac{d}{d x} (x^{3} + y^{3} + z^{3} + 6 x y z - 2)

和/差の法則を適用:

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

= z (\frac{d}{d x} (x^{3}) + \frac{d}{d x} (y^{3}) + \frac{d}{d x} (z^{3}) + \frac{d}{d x} (6 x y z) - \frac{d}{d x} (2))

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (y^{3}) = 0

\frac{d}{d x} (z^{3}) = 0

\frac{d}{d x} (6 x y z) = 6 y z

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

= z (3 x^{2} + 0 + 0 + 6 y z - 0)

簡素化

= z (3 x^{2} + 6 y z)