(\partial)/(\partial y)(4x^3y^2+2)

解

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 2)

8 x^{3} y

解答ステップ

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 2)

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

\frac{\partial}{\partial y} (4 x^{3} y^{2}) = 8 x^{3} y

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

= 8 x^{3} y + 0

簡素化

= 8 x^{3} y