derivative ((3t-1))/(sqrt(t)-2)

解答

导数

\frac{( 3 t - 1 )}{t - 2}

\frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

求解步骤

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

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

\frac{d}{d t} (t - 2) = \frac{1}{2 t}

= \frac{3 ( t - 2 ) - \frac{1}{2 t} ( 3 t - 1 )}{( t - 2 ) ^{2}}

化简

\frac{3 ( t - 2 ) - \frac{1}{2 t} ( 3 t - 1 )}{( t - 2 ) ^{2}} : \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

= \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

t an g e n t y = \frac{4 x}{x + 2}

\frac{d}{d x} (ln (4 x y))

d er i v a t i v e \frac{18}{x ^{4}}

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

d er i v a t i v e (x^{2} - 3 x + 2)^{5}