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

解

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

\frac{1}{y - z}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

簡素化

= \frac{1}{y - z}