derivative of 4/(x^4-5\sqrt[3]{x})

解答

\frac{d}{d x} (\frac{4}{x ^{4}} - 5 3 x)

\frac{- 48 x ^{\frac{2}{3}} - 5 x ^{5}}{3 x ^{\frac{17}{3}}}

求解步骤

\frac{d}{d x} (\frac{4}{x ^{4}} - 5 3 x)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{4}{x ^{4}}) - \frac{d}{d x} (5 3 x)

\frac{d}{d x} (\frac{4}{x ^{4}}) = - \frac{16}{x ^{5}}

\frac{d}{d x} (5 3 x) = \frac{5}{3 x ^{\frac{2}{3}}}

= - \frac{16}{x ^{5}} - \frac{5}{3 x ^{\frac{2}{3}}}

化简

- \frac{16}{x ^{5}} - \frac{5}{3 x ^{\frac{2}{3}}} : \frac{- 48 x ^{\frac{2}{3}} - 5 x ^{5}}{3 x ^{\frac{17}{3}}}

= \frac{- 48 x ^{\frac{2}{3}} - 5 x ^{5}}{3 x ^{\frac{17}{3}}}

\int \frac{5}{x ^{2} + 4} d x

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

x \to \infty lim (\frac{3 ^{x - 3}}{2 ^{n + 3}})

x \to 2 - lim (x + 4)

3 y (x^{2} - 1) d x + (x^{3} + 8 y - 3 x) d y = 0