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

解

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

z (x, y) (4 x y^{3} + 2 x y)

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{d}{d x} (2 x^{2} y^{3}) = 4 x y^{3}

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

= z (x, y) (4 x y^{3} + 2 x y)