derivative f(x)=(x-3)/(5x+2)

解

導関数

f (x) = \frac{x - 3}{5 x + 2}

\frac{17}{( 5 x + 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x - 3}{5 x + 2})

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 - 3 ) ( 5 x + 2 ) - \frac{d}{d x} ( 5 x + 2 ) ( x - 3 )}{( 5 x + 2 ) ^{2}}

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (5 x + 2) = 5

= \frac{1 \cdot ( 5 x + 2 ) - 5 ( x - 3 )}{( 5 x + 2 ) ^{2}}

簡素化

\frac{1 \cdot ( 5 x + 2 ) - 5 ( x - 3 )}{( 5 x + 2 ) ^{2}} : \frac{17}{( 5 x + 2 ) ^{2}}

= \frac{17}{( 5 x + 2 ) ^{2}}