derivative f(x)= x/(x-7)

解

導関数

f (x) = \frac{x}{x - 7}

- \frac{7}{( x - 7 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{x - 7})

商の法則を適用:

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

= \frac{\frac{d x}{d x} ( x - 7 ) - \frac{d}{d x} ( x - 7 ) x}{( x - 7 ) ^{2}}

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

\frac{d}{d x} (x - 7) = 1

= \frac{1 \cdot ( x - 7 ) - 1 \cdot x}{( x - 7 ) ^{2}}

簡素化

\frac{1 \cdot ( x - 7 ) - 1 \cdot x}{( x - 7 ) ^{2}} : - \frac{7}{( x - 7 ) ^{2}}

= - \frac{7}{( x - 7 ) ^{2}}