d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y}))

解

\frac{d}{d x} ((z) (3 x y + z^{2} x - 7 y))

z (z^{2} + 3 y)

解答ステップ

\frac{d}{d x} ((z) (3 x y + z^{2} x - 7 y))

定数を除去:

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

= z \frac{d}{d x} (3 x y + z^{2} x - 7 y)

和/差の法則を適用:

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

= z (\frac{d}{d x} (3 x y) + \frac{d}{d x} (z^{2} x) - \frac{d}{d x} (7 y))

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

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

\frac{d}{d x} (7 y) = 0

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

簡素化

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