(\partial)/(\partial x)((z)(3x^2+6y^2+4))

解

\frac{\partial}{\partial x} ((z) (3 x^{2} + 6 y^{2} + 4))

6 z x

解答ステップ

\frac{\partial}{\partial x} ((z) (3 x^{2} + 6 y^{2} + 4))

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} (3 x^{2} + 6 y^{2} + 4)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (6 y^{2}) + \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (6 y^{2}) = 0

\frac{\partial}{\partial x} (4) = 0

= z (6 x + 0 + 0)

簡素化

= 6 z x