derivative f(x)=(x+9)/(x-9)

解

導関数

f (x) = \frac{x + 9}{x - 9}

- \frac{18}{( x - 9 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x + 9}{x - 9})

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 + 9 ) ( x - 9 ) - \frac{d}{d x} ( x - 9 ) ( x + 9 )}{( x - 9 ) ^{2}}

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (x - 9) = 1

= \frac{1 \cdot ( x - 9 ) - 1 \cdot ( x + 9 )}{( x - 9 ) ^{2}}

簡素化

\frac{1 \cdot ( x - 9 ) - 1 \cdot ( x + 9 )}{( x - 9 ) ^{2}} : - \frac{18}{( x - 9 ) ^{2}}

= - \frac{18}{( x - 9 ) ^{2}}