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

解

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

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

解答ステップ

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

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^{2} z)

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^{2} z))

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

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

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