derivative f(x)=(2x-1)/(4x+8)

解

導関数

f (x) = \frac{2 x - 1}{4 x + 8}

\frac{5}{4 ( x + 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 x - 1}{4 x + 8})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 2 x - 1 ) ( 4 x + 8 ) - \frac{d}{d x} ( 4 x + 8 ) ( 2 x - 1 )}{( 4 x + 8 ) ^{2}}

\frac{d}{d x} (2 x - 1) = 2

\frac{d}{d x} (4 x + 8) = 4

= \frac{2 ( 4 x + 8 ) - 4 ( 2 x - 1 )}{( 4 x + 8 ) ^{2}}

簡素化

\frac{2 ( 4 x + 8 ) - 4 ( 2 x - 1 )}{( 4 x + 8 ) ^{2}} : \frac{5}{4 ( x + 2 ) ^{2}}

= \frac{5}{4 ( x + 2 ) ^{2}}