(\partial)/(\partial y)(5x^2+y^2)

解

\frac{\partial}{\partial y} (5 x^{2} + y^{2})

2 y

解答ステップ

\frac{\partial}{\partial y} (5 x^{2} + y^{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} (5 x^{2}) + \frac{\partial}{\partial y} (y^{2})

\frac{\partial}{\partial y} (5 x^{2}) = 0

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

= 0 + 2 y

簡素化

= 2 y