derivative f(x)= x/((x-7)^2)

解

導関数

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

\frac{- 7 - x}{( x - 7 ) ^{3}}

解答ステップ

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

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

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

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

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

簡素化

\frac{1 \cdot ( x - 7 ) ^{2} - 2 ( x - 7 ) x}{( ( x - 7 ) ^{2} ) ^{2}} : \frac{- 7 - x}{( x - 7 ) ^{3}}

= \frac{- 7 - x}{( x - 7 ) ^{3}}