(\partial)/(\partial x)((z)(x^4y+xz+yz^2))

解

\frac{\partial}{\partial x} ((z) (x^{4} y + x z + y z^{2}))

z (z + 4 x^{3} y)

解答ステップ

\frac{\partial}{\partial x} ((z) (x^{4} y + x z + y z^{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^{4} y + x z + y z^{2})

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (x^{4} y) + \frac{\partial}{\partial x} (x z) + \frac{\partial}{\partial x} (y z^{2}))

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

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

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

= z (4 y x^{3} + z + 0)

簡素化

= z (z + 4 x^{3} y)