(\partial)/(\partial x)(yx^2z^2-xy^4+xz)

解

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

2 y z^{2} x - y^{4} + z

解答ステップ

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

y, z

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

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

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

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

= 2 y z^{2} x - y^{4} + z