derivative of (-11/(2(x-2)^2)-4/(x-2))

解答

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}} - \frac{4}{x - 2})

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

求解步骤

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}} - \frac{4}{x - 2})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}}) - \frac{d}{d x} (\frac{4}{x - 2})

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}}) = \frac{11}{( x - 2 ) ^{3}}

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

= \frac{11}{( x - 2 ) ^{3}} - (- \frac{4}{( x - 2 ) ^{2}})

化简

\frac{11}{( x - 2 ) ^{3}} - (- \frac{4}{( x - 2 ) ^{2}}) : \frac{4 x + 3}{( x - 2 ) ^{3}}

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

in v erse l a pl a ce \frac{2 s + 3}{s ^{2} + 17}

\int x + 1 + \frac{2}{3} x d x

x \to + 0 + lim (\frac{2}{1 + ln ( x )})

d er i v a t i v e y = 4 x - x^{2}

\int 20 t (5 t^{2} - 3)^{3} d t