(\partial)/(\partial x)(x^3-6xy+y^3-2)

解

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

3 x^{2} - 6 y

解答ステップ

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

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

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

\frac{\partial}{\partial x} (6 x y) = 6 y

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

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

= 3 x^{2} - 6 y + 0 - 0

簡素化

= 3 x^{2} - 6 y