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

解

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

4 z^{2} x^{2} y^{3}

解答ステップ

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

z, x

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial y} (x^{2} y^{4} z) = 4 z x^{2} y^{3}

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

= z (4 z x^{2} y^{3} + 0)

簡素化

z (4 z x^{2} y^{3} + 0) : 4 z^{2} x^{2} y^{3}

= 4 z^{2} x^{2} y^{3}