d/(dy)((x)(x^3+3y^3+5x+y))

解

\frac{d}{d y} ((x) (x^{3} + 3 y^{3} + 5 x + y))

x (9 y^{2} + 1)

解答ステップ

\frac{d}{d y} ((x) (x^{3} + 3 y^{3} + 5 x + y))

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^{3} + 3 y^{3} + 5 x + y)

和/差の法則を適用:

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

= x (\frac{d}{d y} (x^{3}) + \frac{d}{d y} (3 y^{3}) + \frac{d}{d y} (5 x) + \frac{d y}{d y})

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

\frac{d}{d y} (3 y^{3}) = 9 y^{2}

\frac{d}{d y} (5 x) = 0

\frac{d y}{d y} = 1

= x (0 + 9 y^{2} + 0 + 1)

簡素化

= x (9 y^{2} + 1)