derivative f(x)=(3x-1)/(x+2)

解答

导数

f (x) = \frac{3 x - 1}{x + 2}

\frac{7}{( x + 2 ) ^{2}}

求解步骤

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

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

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

\frac{d}{d x} (x + 2) = 1

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

化简

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

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

d er i v a t i v e \frac{4}{t}

\int_{0}^{6} \frac{1}{x - 3} d x

p a r t ia l f r a c t i o n \frac{x ^{2}}{3 x + 1}

\int cos (\frac{nπ x}{2 π}) d x

x \to 2 - lim (\frac{3}{2 - x})