(\partial)/(\partial y)(6xy-2+10x^2y)

解

\frac{\partial}{\partial y} (6 x y - 2 + 10 x^{2} y)

10 x^{2} + 6 x

解答ステップ

\frac{\partial}{\partial y} (6 x y - 2 + 10 x^{2} y)

x

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 y} (6 x y) - \frac{\partial}{\partial y} (2) + \frac{\partial}{\partial y} (10 x^{2} y)

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

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

\frac{\partial}{\partial y} (10 x^{2} y) = 10 x^{2}

= 6 x - 0 + 10 x^{2}

簡素化

= 10 x^{2} + 6 x