derivative g(x)=((9+6x)/(7-4x))

解答

导数

g (x) = (\frac{9 + 6 x}{7 - 4 x})

\frac{78}{( 7 - 4 x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{9 + 6 x}{7 - 4 x})

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} ( 9 + 6 x ) ( 7 - 4 x ) - \frac{d}{d x} ( 7 - 4 x ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}}

\frac{d}{d x} (9 + 6 x) = 6

\frac{d}{d x} (7 - 4 x) = - 4

= \frac{6 ( 7 - 4 x ) - ( - 4 ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}}

化简

\frac{6 ( 7 - 4 x ) - ( - 4 ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}} : \frac{78}{( 7 - 4 x ) ^{2}}

= \frac{78}{( 7 - 4 x ) ^{2}}

\frac{\partial}{\partial z} (\frac{y}{z})

\frac{d}{d x} ((A x^{2} + B x) e^{- x})

\frac{d}{d t} (\frac{2 t}{t ^{2} + 2})

d er i v a t i v e arccot (3 x)

n = 1 \sum \infty \frac{n !}{1 4 ^{n}}