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

解

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

- \frac{n - 1}{x ^{2}}

解答ステップ

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

n, y

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

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

= (n - 1) (- \frac{1}{x ^{2}} - 0)

簡素化

(n - 1) (- \frac{1}{x ^{2}} - 0) : - \frac{n - 1}{x ^{2}}

= - \frac{n - 1}{x ^{2}}