d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y}))

解

\frac{d}{d y} ((z (y, x)) (x y^{5} - x^{2} y))

z (y, x) (5 y^{4} x - x^{2})

解答ステップ

\frac{d}{d y} ((z (y, x)) (x y^{5} - x^{2} y))

定数を除去:

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

= z (y, x) \frac{d}{d y} (x y^{5} - x^{2} y)

和/差の法則を適用:

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

= z (y, x) (\frac{d}{d y} (x y^{5}) - \frac{d}{d y} (x^{2} y))

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

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

= z (y, x) (5 y^{4} x - x^{2})