derivative ((3x+5)(2x-7))/(8x^2-3)

解答

导数

\frac{( 3 x + 5 ) ( 2 x - 7 )}{8 x ^{2} - 3}

\frac{88 x ^{2} + 524 x + 33}{( 8 x ^{2} - 3 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{( 3 x + 5 ) ( 2 x - 7 )}{8 x ^{2} - 3})

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} ( ( 3 x + 5 ) ( 2 x - 7 ) ) ( 8 x ^{2} - 3 ) - \frac{d}{d x} ( 8 x ^{2} - 3 ) ( 3 x + 5 ) ( 2 x - 7 )}{( 8 x ^{2} - 3 ) ^{2}}

\frac{d}{d x} ((3 x + 5) (2 x - 7)) = 12 x - 11

\frac{d}{d x} (8 x^{2} - 3) = 16 x

= \frac{( 12 x - 11 ) ( 8 x ^{2} - 3 ) - 16 x ( 3 x + 5 ) ( 2 x - 7 )}{( 8 x ^{2} - 3 ) ^{2}}

乘开

(12 x - 11) (8 x^{2} - 3) - 16 x (3 x + 5) (2 x - 7) : 88 x^{2} + 524 x + 33

= \frac{88 x ^{2} + 524 x + 33}{( 8 x ^{2} - 3 ) ^{2}}

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