derivative f(x)=(x+2)/(10-3x)

解

導関数

f (x) = \frac{x + 2}{10 - 3 x}

\frac{16}{( 10 - 3 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x + 2}{10 - 3 x})

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 + 2 ) ( 10 - 3 x ) - \frac{d}{d x} ( 10 - 3 x ) ( x + 2 )}{( 10 - 3 x ) ^{2}}

\frac{d}{d x} (x + 2) = 1

\frac{d}{d x} (10 - 3 x) = - 3

= \frac{1 \cdot ( 10 - 3 x ) - ( - 3 ) ( x + 2 )}{( 10 - 3 x ) ^{2}}

簡素化

\frac{1 \cdot ( 10 - 3 x ) - ( - 3 ) ( x + 2 )}{( 10 - 3 x ) ^{2}} : \frac{16}{( 10 - 3 x ) ^{2}}

= \frac{16}{( 10 - 3 x ) ^{2}}