d/(dy)((x(y))(y^2+y))

解

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

x (3 y^{2} + 2 y)

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = y^{2} + y

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

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

\frac{d}{d y} (y^{2} + y) = 2 y + 1

= x (1 \cdot (y^{2} + y) + (2 y + 1) y)

簡素化

x (1 \cdot (y^{2} + y) + (2 y + 1) y) : x (3 y^{2} + 2 y)

= x (3 y^{2} + 2 y)