derivative of (3x-4/(6x^2-1))

解

\frac{d}{d x} (\frac{3 x - 4}{6 x ^{2} - 1})

\frac{- 18 x ^{2} + 48 x - 3}{( 6 x ^{2} - 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{3 x - 4}{6 x ^{2} - 1})

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 - 4 ) ( 6 x ^{2} - 1 ) - \frac{d}{d x} ( 6 x ^{2} - 1 ) ( 3 x - 4 )}{( 6 x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (3 x - 4) = 3

\frac{d}{d x} (6 x^{2} - 1) = 12 x

= \frac{3 ( 6 x ^{2} - 1 ) - 12 x ( 3 x - 4 )}{( 6 x ^{2} - 1 ) ^{2}}

拡張

3 (6 x^{2} - 1) - 12 x (3 x - 4) : - 18 x^{2} + 48 x - 3

= \frac{- 18 x ^{2} + 48 x - 3}{( 6 x ^{2} - 1 ) ^{2}}