derivative of 4x^{2/3}+x^{5/3}

解答

\frac{d}{d x} (4 x^{\frac{2}{3}} + x^{\frac{5}{3}})

\frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

求解步骤

\frac{d}{d x} (4 x^{\frac{2}{3}} + x^{\frac{5}{3}})

使用微分加减法定则:

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

= \frac{d}{d x} (4 x^{\frac{2}{3}}) + \frac{d}{d x} (x^{\frac{5}{3}})

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

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

= \frac{8}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3}

化简

\frac{8}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3} : \frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

= \frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

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

\frac{d y}{d x} + 5 (tan (5 x)) y = 3 cos (5 x)

\int 60 x^{2} (1 - 4 x^{3})^{4} d x

d er i v a t i v e f (x) = 3 e^{2 x} + x^{3}

d er i v a t i v e f (x) = x^{\frac{5}{6}}