derivative of (2x+3/(x+4))

解

\frac{d}{d x} (\frac{2 x + 3}{x + 4})

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

解答ステップ

\frac{d}{d x} (\frac{2 x + 3}{x + 4})

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 + 3 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( 2 x + 3 )}{( x + 4 ) ^{2}}

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

\frac{d}{d x} (x + 4) = 1

= \frac{2 ( x + 4 ) - 1 \cdot ( 2 x + 3 )}{( x + 4 ) ^{2}}

簡素化

\frac{2 ( x + 4 ) - 1 \cdot ( 2 x + 3 )}{( x + 4 ) ^{2}} : \frac{5}{( x + 4 ) ^{2}}

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