derivative 3/(x^2)-8\sqrt[4]{x}

解答

导数

\frac{3}{x ^{2}} - 8 4 x

\frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}

求解步骤

\frac{d}{d x} (\frac{3}{x ^{2}} - 8 4 x)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{3}{x ^{2}}) - \frac{d}{d x} (8 4 x)

\frac{d}{d x} (\frac{3}{x ^{2}}) = - \frac{6}{x ^{3}}

\frac{d}{d x} (8 4 x) = \frac{2}{x ^{\frac{3}{4}}}

= - \frac{6}{x ^{3}} - \frac{2}{x ^{\frac{3}{4}}}

化简

- \frac{6}{x ^{3}} - \frac{2}{x ^{\frac{3}{4}}} : \frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}

= \frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}

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

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

y^{^{'''}} - 8 = 0

n = 0 \sum \infty \frac{2 n}{n ^{2}}

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