derivative f(x)=(x-5)/x

解

導関数

f (x) = \frac{x - 5}{x}

\frac{5}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x - 5}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x - 5 ) x - \frac{d x}{d x} ( x - 5 )}{x ^{2}}

\frac{d}{d x} (x - 5) = 1

\frac{d x}{d x} = 1

= \frac{1 \cdot x - 1 \cdot ( x - 5 )}{x ^{2}}

簡素化

\frac{1 \cdot x - 1 \cdot ( x - 5 )}{x ^{2}} : \frac{5}{x ^{2}}

= \frac{5}{x ^{2}}