derivative \sqrt[3]{x}+1/(x^2)

解答

导数

3 x + \frac{1}{x ^{2}}

\frac{x ^{3} - 6 x ^{\frac{2}{3}}}{3 x ^{\frac{11}{3}}}

求解步骤

\frac{d}{d x} (3 x + \frac{1}{x ^{2}})

使用微分加减法定则:

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

= \frac{d}{d x} (3 x) + \frac{d}{d x} (\frac{1}{x ^{2}})

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

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

= \frac{1}{3 x ^{\frac{2}{3}}} - \frac{2}{x ^{3}}

化简

\frac{1}{3 x ^{\frac{2}{3}}} - \frac{2}{x ^{3}} : \frac{x ^{3} - 6 x ^{\frac{2}{3}}}{3 x ^{\frac{11}{3}}}

= \frac{x ^{3} - 6 x ^{\frac{2}{3}}}{3 x ^{\frac{11}{3}}}

\frac{\partial}{\partial x} (- \frac{1}{( 10 + x \cdot y )})

d er i v a t i v e x (8^{- 2 x})

l a pl a ce t r an s f or m \frac{3}{2} sin (2 t)

x \to 3 lim (\frac{1}{x - 3})

f (x) = cos^{2} (2 - x^{2})