(\partial)/(\partial x)(6x^3y+6y^5+1)

解

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

18 x^{2} y

解答ステップ

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

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} (6 x^{3} y) + \frac{\partial}{\partial x} (6 y^{5}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (6 x^{3} y) = 18 y x^{2}

\frac{\partial}{\partial x} (6 y^{5}) = 0

\frac{\partial}{\partial x} (1) = 0

= 18 y x^{2} + 0 + 0

簡素化

= 18 x^{2} y