derivative of 2x^{4/3}-3x^{2/3}

解答

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

\frac{8 x ^{\frac{1}{3}}}{3} - \frac{2}{x ^{\frac{1}{3}}}

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (2 x^{\frac{4}{3}}) = \frac{8 x ^{\frac{1}{3}}}{3}

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

= \frac{8 x ^{\frac{1}{3}}}{3} - \frac{2}{x ^{\frac{1}{3}}}

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

\int 2 cos^{3} (x) d x

\int (2 x - \frac{1}{8 x})^{2} d x

\frac{d}{d x} (\frac{x ^{3}}{9} + \frac{3}{4 x})

a re a 9 (x^{3} - x), 0