d/(d{x)}(({z}(x,y))(6{x}^5+4{y}^3+4{y}))

解

\frac{d}{d x} ((z (x, y)) (6 x^{5} + 4 y^{3} + 4 y))

z (x, y) (30 x^{4} + 0 + 0)

解答ステップ

\frac{d}{d x} ((z (x, y)) (6 x^{5} + 4 y^{3} + 4 y))

定数を除去:

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

= z (x, y) \frac{d}{d x} (6 x^{5} + 4 y^{3} + 4 y)

和/差の法則を適用:

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

= z (x, y) (\frac{d}{d x} (6 x^{5}) + \frac{d}{d x} (4 y^{3}) + \frac{d}{d x} (4 y))

\frac{d}{d x} (6 x^{5}) = 30 x^{4}

\frac{d}{d x} (4 y^{3}) = 0

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

= z (x, y) (30 x^{4} + 0 + 0)