derivative (7x^2-6x+4)/(3x+8)

解

導関数

\frac{7 x ^{2} - 6 x + 4}{3 x + 8}

\frac{21 x ^{2} + 112 x - 60}{( 3 x + 8 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{7 x ^{2} - 6 x + 4}{3 x + 8})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} - 6 x + 4 ) ( 3 x + 8 ) - \frac{d}{d x} ( 3 x + 8 ) ( 7 x ^{2} - 6 x + 4 )}{( 3 x + 8 ) ^{2}}

\frac{d}{d x} (7 x^{2} - 6 x + 4) = 14 x - 6

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

= \frac{( 14 x - 6 ) ( 3 x + 8 ) - 3 ( 7 x ^{2} - 6 x + 4 )}{( 3 x + 8 ) ^{2}}

拡張

(14 x - 6) (3 x + 8) - 3 (7 x^{2} - 6 x + 4) : 21 x^{2} + 112 x - 60

= \frac{21 x ^{2} + 112 x - 60}{( 3 x + 8 ) ^{2}}