(\partial)/(\partial y)(15x^2-9xy+25y^2)

解

\frac{\partial}{\partial y} (15 x^{2} - 9 x y + 25 y^{2})

50 y - 9 x

解答ステップ

\frac{\partial}{\partial y} (15 x^{2} - 9 x y + 25 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} (15 x^{2}) - \frac{\partial}{\partial y} (9 x y) + \frac{\partial}{\partial y} (25 y^{2})

\frac{\partial}{\partial y} (15 x^{2}) = 0

\frac{\partial}{\partial y} (9 x y) = 9 x

\frac{\partial}{\partial y} (25 y^{2}) = 50 y

= 0 - 9 x + 50 y

簡素化

= 50 y - 9 x