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

解

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

2 x y

解答ステップ

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

x

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

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

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

= x (0 + 2 y)

簡素化

= 2 x y