derivative of (2x^2+x-3/(2x+7))

解答

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

\frac{4 x ^{2} + 28 x + 13}{( 2 x + 7 ) ^{2}}

求解步骤

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

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

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

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

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

乘开

(4 x + 1) (2 x + 7) - 2 (2 x^{2} + x - 3) : 4 x^{2} + 28 x + 13

= \frac{4 x ^{2} + 28 x + 13}{( 2 x + 7 ) ^{2}}

\int x^{2} e^{2} d x

t an g e n t f (x) = x^{2} + 2, (3, 11)

\frac{d y}{d x} = (3 x)

\frac{d}{d x} (cot (4 x^{2}) (x^{2} - 9))

n = 1 \sum \infty \frac{n + 4}{3 n + 2}