derivative of (3x-9/(2x+4))

解答

\frac{d}{d x} (\frac{3 x - 9}{2 x + 4})

\frac{15}{2 ( x + 2 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{3 x - 9}{2 x + 4})

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 - 9 ) ( 2 x + 4 ) - \frac{d}{d x} ( 2 x + 4 ) ( 3 x - 9 )}{( 2 x + 4 ) ^{2}}

\frac{d}{d x} (3 x - 9) = 3

\frac{d}{d x} (2 x + 4) = 2

= \frac{3 ( 2 x + 4 ) - 2 ( 3 x - 9 )}{( 2 x + 4 ) ^{2}}

化简

\frac{3 ( 2 x + 4 ) - 2 ( 3 x - 9 )}{( 2 x + 4 ) ^{2}} : \frac{15}{2 ( x + 2 ) ^{2}}

= \frac{15}{2 ( x + 2 ) ^{2}}

\int \frac{1}{16 x ^{2} + 25} d x

\int 15 - 2 x - x^{2} d x

\frac{d y}{d t} + k (340 - y) = 0

l a pl a ce t r an s f or m e

\int - 4 x^{2} (4 x^{3} - 1)^{7} d x