derivative (3x+8)/(x^2)

解

導関数

\frac{3 x + 8}{x ^{2}}

\frac{- 3 x - 16}{x ^{3}}

解答ステップ

\frac{d}{d x} (\frac{3 x + 8}{x ^{2}})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 3 x + 8 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x + 8 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x + 8) = 3

\frac{d}{d x} (x^{2}) = 2 x

= \frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}}

簡素化

\frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}} : \frac{- 3 x - 16}{x ^{3}}

= \frac{- 3 x - 16}{x ^{3}}