(\partial)/(\partial y)(y+3xy^2-18)

解

\frac{\partial}{\partial y} (y + 3 x y^{2} - 18)

6 y x + 1

解答ステップ

\frac{\partial}{\partial y} (y + 3 x y^{2} - 18)

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} (y) + \frac{\partial}{\partial y} (3 x y^{2}) - \frac{\partial}{\partial y} (18)

\frac{\partial}{\partial y} (y) = 1

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

\frac{\partial}{\partial y} (18) = 0

= 1 + 6 x y - 0

簡素化

= 6 y x + 1