derivative of ((x+1(3x-7))/(3x+1))

解答

\frac{d}{d x} (\frac{( x + 1 ) ( 3 x - 7 )}{3 x + 1})

\frac{9 x ^{2} + 6 x + 17}{( 3 x + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{( x + 1 ) ( 3 x - 7 )}{3 x + 1})

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} ( ( x + 1 ) ( 3 x - 7 ) ) ( 3 x + 1 ) - \frac{d}{d x} ( 3 x + 1 ) ( x + 1 ) ( 3 x - 7 )}{( 3 x + 1 ) ^{2}}

\frac{d}{d x} ((x + 1) (3 x - 7)) = 6 x - 4

\frac{d}{d x} (3 x + 1) = 3

= \frac{( 6 x - 4 ) ( 3 x + 1 ) - 3 ( x + 1 ) ( 3 x - 7 )}{( 3 x + 1 ) ^{2}}

乘开

(6 x - 4) (3 x + 1) - 3 (x + 1) (3 x - 7) : 9 x^{2} + 6 x + 17

= \frac{9 x ^{2} + 6 x + 17}{( 3 x + 1 ) ^{2}}

\int_{- 2}^{2} (x^{2} - 2)^{2} d x

\frac{d}{d x} (1 - (1 - 0.01 x)^{3})

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

d er i v a t i v e f (x) = 1 - \frac{1}{x}

a re a y^{2} = x + 10, y^{2} = 8 - x