derivative of (7x+8/(4x+8))

解

\frac{d}{d x} (\frac{7 x + 8}{4 x + 8})

\frac{3}{2 ( x + 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{7 x + 8}{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} ( 7 x + 8 ) ( 4 x + 8 ) - \frac{d}{d x} ( 4 x + 8 ) ( 7 x + 8 )}{( 4 x + 8 ) ^{2}}

\frac{d}{d x} (7 x + 8) = 7

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

= \frac{7 ( 4 x + 8 ) - 4 ( 7 x + 8 )}{( 4 x + 8 ) ^{2}}

簡素化

\frac{7 ( 4 x + 8 ) - 4 ( 7 x + 8 )}{( 4 x + 8 ) ^{2}} : \frac{3}{2 ( x + 2 ) ^{2}}

= \frac{3}{2 ( x + 2 ) ^{2}}