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

解

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

z (x, y) (2 x + 0 + y)

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

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

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

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

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

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

= z (x, y) (2 x + 0 + y)