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

解

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

\frac{3}{y + 3 z}

解答ステップ

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

z, y

を定数として扱う

定数を除去:

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

= \frac{1}{y + 3 z} \frac{\partial}{\partial x} (3 x - 3 z)

和/差の法則を適用:

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

= \frac{1}{y + 3 z} (\frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (3 z))

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

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

= \frac{1}{y + 3 z} (3 - 0)

簡素化

\frac{1}{y + 3 z} (3 - 0) : \frac{3}{y + 3 z}

= \frac{3}{y + 3 z}