(\partial)/(\partial x)((z)(3xz-z^3+yz))

解

\frac{\partial}{\partial x} ((z) (3 x z - z^{3} + yz))

3 z^{2}

解答ステップ

\frac{\partial}{\partial x} ((z) (3 x z - z^{3} + yz))

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} (3 x z - z^{3} + yz)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (3 x z) - \frac{\partial}{\partial x} (z^{3}) + \frac{\partial}{\partial x} (yz))

\frac{\partial}{\partial x} (3 x z) = 3 z

\frac{\partial}{\partial x} (z^{3}) = 0

\frac{\partial}{\partial x} (yz) = 0

= z (3 z - 0 + 0)

簡素化

z (3 z - 0 + 0) : 3 z^{2}

= 3 z^{2}