derivative y=(3x-1)/(6x+5)

解答

导数

y = \frac{3 x - 1}{6 x + 5}

\frac{21}{( 6 x + 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{3 x - 1}{6 x + 5})

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 - 1 ) ( 6 x + 5 ) - \frac{d}{d x} ( 6 x + 5 ) ( 3 x - 1 )}{( 6 x + 5 ) ^{2}}

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

\frac{d}{d x} (6 x + 5) = 6

= \frac{3 ( 6 x + 5 ) - 6 ( 3 x - 1 )}{( 6 x + 5 ) ^{2}}

乘开

3 (6 x + 5) - 6 (3 x - 1) : 21

= \frac{21}{( 6 x + 5 ) ^{2}}

d er i v a t i v e f (x) = (6 x^{2} - x + 7)^{- \frac{5}{3}}

\frac{d y}{d t} = k (y - 60)

\int \frac{x}{( 4 x + 5 ) ^{2}} d x

x \to 1 lim ((x^{3} + 2) (3 - x))

x \to 3 lim (\frac{( 4 x ^{2} + 3 x )}{5})