(\partial)/(\partial x)((z)(x^2y+4x+3y))

解

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

z (2 x y + 4)

解答ステップ

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

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^{2} y + 4 x + 3 y)

和/差の法則を適用:

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

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

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

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

\frac{\partial}{\partial x} (3 y) = 0

= z (2 y x + 4 + 0)

簡素化

= z (2 x y + 4)