d/(dy)((x)(x^2+y^2-4x+10y-12))

解

\frac{d}{d y} ((x) (x^{2} + y^{2} - 4 x + 10 y - 12))

x (2 y + 10)

解答ステップ

\frac{d}{d y} ((x) (x^{2} + y^{2} - 4 x + 10 y - 12))

x

を定数として扱う

定数を除去:

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

= x \frac{d}{d y} (x^{2} + y^{2} - 4 x + 10 y - 12)

和/差の法則を適用:

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

= x (\frac{d}{d y} (x^{2}) + \frac{d}{d y} (y^{2}) - \frac{d}{d y} (4 x) + \frac{d}{d y} (10 y) - \frac{d}{d y} (12))

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

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

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

\frac{d}{d y} (10 y) = 10

\frac{d}{d y} (12) = 0

= x (0 + 2 y - 0 + 10 - 0)

簡素化

= x (2 y + 10)