(\partial)/(\partial x)(x^7-6xy-3y^2)

解

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{2})

7 x^{6} - 6 y

解答ステップ

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{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^{7}) - \frac{\partial}{\partial x} (6 x y) - \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (x^{7}) = 7 x^{6}

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 7 x^{6} - 6 y - 0

簡素化

= 7 x^{6} - 6 y