derivative g(x)=((3x-2))/((x^2+2))

解

導関数

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

\frac{- 3 x ^{2} + 4 x + 6}{( x ^{2} + 2 ) ^{2}}

解答ステップ

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

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

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

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

拡張

3 (x^{2} + 2) - 2 x (3 x - 2) : - 3 x^{2} + 4 x + 6

= \frac{- 3 x ^{2} + 4 x + 6}{( x ^{2} + 2 ) ^{2}}