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

解

導関数

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

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

解答ステップ

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

商の法則を適用:

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

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

\frac{d x}{d x} = 1

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

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

1 \cdot (x + 5) - 1 \cdot x = 5

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