derivative f(x)=(7x-4)/(-3x+3)

解答

导数

f (x) = \frac{7 x - 4}{- 3 x + 3}

\frac{1}{( x - 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{7 x - 4}{- 3 x + 3})

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

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

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

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

化简

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

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

\int \frac{5}{x ^{2} + 18 x + 82} d x

\int_{0}^{13} \frac{1}{x ^{\frac{1}{4}}} d x

n \to \infty lim (a^{n})

y^{^{'}} = x y^{2} + 2 y^{2}

y^{^{''}} + 4 y = 8 sin (2 t)