derivative of (5x^2-9x+8/(7x+2))

解答

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 8}{7 x + 2})

\frac{35 x ^{2} + 20 x - 74}{( 7 x + 2 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 8}{7 x + 2})

使用微分除法定则:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} - 9 x + 8 ) ( 7 x + 2 ) - \frac{d}{d x} ( 7 x + 2 ) ( 5 x ^{2} - 9 x + 8 )}{( 7 x + 2 ) ^{2}}

\frac{d}{d x} (5 x^{2} - 9 x + 8) = 10 x - 9

\frac{d}{d x} (7 x + 2) = 7

= \frac{( 10 x - 9 ) ( 7 x + 2 ) - 7 ( 5 x ^{2} - 9 x + 8 )}{( 7 x + 2 ) ^{2}}

乘开

(10 x - 9) (7 x + 2) - 7 (5 x^{2} - 9 x + 8) : 35 x^{2} + 20 x - 74

= \frac{35 x ^{2} + 20 x - 74}{( 7 x + 2 ) ^{2}}