(\partial)/(\partial x)(1-y/x)

解

\frac{\partial}{\partial x} (1 - \frac{y}{x})

\frac{y}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (1 - \frac{y}{x})

y

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} (1) - \frac{\partial}{\partial x} (\frac{y}{x})

\frac{\partial}{\partial x} (1) = 0

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

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

簡素化

= \frac{y}{x ^{2}}