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

解

導関数

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

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

解答ステップ

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

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

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

\frac{d}{d x} (x + 5) = 1

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

簡素化

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

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