(\partial)/(\partial x)((z)(16-x^2-y^2))

解

\frac{\partial}{\partial x} ((z) (16 - x^{2} - y^{2}))

- 2 z x

解答ステップ

\frac{\partial}{\partial x} ((z) (16 - x^{2} - y^{2}))

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} (16 - x^{2} - y^{2})

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (16) - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2}))

\frac{\partial}{\partial x} (16) = 0

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

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

= z (0 - 2 x - 0)

簡素化

= - 2 z x