(\partial)/(\partial y)((z)(-3x+5y+z))

解

\frac{\partial}{\partial y} ((z) (- 3 x + 5 y + z))

5 z

解答ステップ

\frac{\partial}{\partial y} ((z) (- 3 x + 5 y + z))

z, x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial y} (- 3 x + 5 y + z)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (- \frac{\partial}{\partial y} (3 x) + \frac{\partial}{\partial y} (5 y) + \frac{\partial}{\partial y} (z))

\frac{\partial}{\partial y} (3 x) = 0

\frac{\partial}{\partial y} (5 y) = 5

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

= z (- 0 + 5 + 0)

簡素化

= 5 z