(\partial)/(\partial x)(xz-5x^2y^3z^4)

解

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

z - 10 z^{4} y^{3} x

解答ステップ

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

z, y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (x z) - \frac{\partial}{\partial x} (5 x^{2} y^{3} z^{4})

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

\frac{\partial}{\partial x} (5 x^{2} y^{3} z^{4}) = 10 z^{4} y^{3} x

= z - 10 z^{4} y^{3} x