(\partial)/(\partial x)(-7x^2+7y^2-7)

解

\frac{\partial}{\partial x} (- 7 x^{2} + 7 y^{2} - 7)

- 14 x

解答ステップ

\frac{\partial}{\partial x} (- 7 x^{2} + 7 y^{2} - 7)

y

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} (7 x^{2}) + \frac{\partial}{\partial x} (7 y^{2}) - \frac{\partial}{\partial x} (7)

\frac{\partial}{\partial x} (7 x^{2}) = 14 x

\frac{\partial}{\partial x} (7 y^{2}) = 0

\frac{\partial}{\partial x} (7) = 0

= - 14 x + 0 - 0

簡素化

= - 14 x