derivative 1/x+1/(x^3)-4/(sqrt(x))

解答

导数

\frac{1}{x} + \frac{1}{x ^{3}} - \frac{4}{x}

\frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

求解步骤

\frac{d}{d x} (\frac{1}{x} + \frac{1}{x ^{3}} - \frac{4}{x})

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{1}{x}) + \frac{d}{d x} (\frac{1}{x ^{3}}) - \frac{d}{d x} (\frac{4}{x})

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

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

= - \frac{1}{x ^{2}} - \frac{3}{x ^{4}} - (- \frac{2}{x ^{\frac{3}{2}}})

化简

- \frac{1}{x ^{2}} - \frac{3}{x ^{4}} - (- \frac{2}{x ^{\frac{3}{2}}}) : \frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

= \frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

\frac{d}{d x} (\frac{x}{x ^{2} - x + 25})

\frac{d}{d t} (t^{n} e^{a t})

\int (3 x + 4)^{2} d x

x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

x \to 0 lim (- 2 x^{2})