(\partial)/(\partial x)(3xy+4xz+5yz-3)

解

\frac{\partial}{\partial x} (3 x y + 4 x z + 5 yz - 3)

3 y + 4 z

解答ステップ

\frac{\partial}{\partial x} (3 x y + 4 x z + 5 yz - 3)

y, z

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 x} (3 x y) + \frac{\partial}{\partial x} (4 x z) + \frac{\partial}{\partial x} (5 yz) - \frac{\partial}{\partial x} (3)

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

\frac{\partial}{\partial x} (4 x z) = 4 z

\frac{\partial}{\partial x} (5 yz) = 0

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

= 3 y + 4 z + 0 - 0

簡素化

= 3 y + 4 z