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

解

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

z (8 x + 3)

解答ステップ

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= z (8 x + 0 + 3)

簡素化

= z (8 x + 3)