derivative of x^{4/3}+4x^{1/3}

解答

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

\frac{4 x + 4}{3 x ^{\frac{2}{3}}}

求解步骤

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

使用微分加减法定则:

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

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

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

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

= \frac{4 x ^{\frac{1}{3}}}{3} + \frac{4}{3 x ^{\frac{2}{3}}}

化简

\frac{4 x ^{\frac{1}{3}}}{3} + \frac{4}{3 x ^{\frac{2}{3}}} : \frac{4 x + 4}{3 x ^{\frac{2}{3}}}

= \frac{4 x + 4}{3 x ^{\frac{2}{3}}}

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

t an g e n t f (x) = x^{2} - 3, (4, 13)

x \to 0 + lim (\frac{7}{x} - \frac{7}{∣ x ∣})

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

in v erse l a pl a ce \frac{s ^{2}}{( s - 3 ) ^{2}}