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

解

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

z (2 x + y)

解答ステップ

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

z, y

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

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

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

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

= z (2 x + y + 0)

簡素化

= z (2 x + y)