(\partial)/(\partial y)((x-y)^2y)

解

\frac{\partial}{\partial y} ((x - y)^{2} y)

3 y^{2} - 4 x y + x^{2}

解答ステップ

\frac{\partial}{\partial y} ((x - y)^{2} y)

x

を定数として扱う

積の法則を適用:

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

f = (x - y)^{2}, g = y

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

\frac{\partial}{\partial y} ((x - y)^{2}) = - 2 (x - y)

\frac{\partial}{\partial y} (y) = 1

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

簡素化

(- 2 (x - y)) y + 1 \cdot (x - y)^{2} : 3 y^{2} - 4 x y + x^{2}

= 3 y^{2} - 4 x y + x^{2}