(\partial)/(\partial x)(12xy-x^3-y^3-7)

解

\frac{\partial}{\partial x} (12 x y - x^{3} - y^{3} - 7)

12 y - 3 x^{2}

解答ステップ

\frac{\partial}{\partial x} (12 x y - x^{3} - y^{3} - 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} (12 x y) - \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (7)

\frac{\partial}{\partial x} (12 x y) = 12 y

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

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

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

= 12 y - 3 x^{2} - 0 - 0

簡素化

= 12 y - 3 x^{2}