(\partial)/(\partial x)((z)(yz-z^2+xny))

解

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

n zy

解答ステップ

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

n, 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} (yz - z^{2} + x n y)

和/差の法則を適用:

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

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

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

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

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

= z (0 - 0 + y n)

簡素化

= n zy