derivative (10x+1)/(x+100)

解

導関数

\frac{10 x + 1}{x + 100}

\frac{999}{( x + 100 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{10 x + 1}{x + 100})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 10 x + 1 ) ( x + 100 ) - \frac{d}{d x} ( x + 100 ) ( 10 x + 1 )}{( x + 100 ) ^{2}}

\frac{d}{d x} (10 x + 1) = 10

\frac{d}{d x} (x + 100) = 1

= \frac{10 ( x + 100 ) - 1 \cdot ( 10 x + 1 )}{( x + 100 ) ^{2}}

簡素化

\frac{10 ( x + 100 ) - 1 \cdot ( 10 x + 1 )}{( x + 100 ) ^{2}} : \frac{999}{( x + 100 ) ^{2}}

= \frac{999}{( x + 100 ) ^{2}}