derivative f(x)=-7x^{4/3}+4/(x^3)

解答

导数

f (x) = - 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}}

\frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

求解步骤

\frac{d}{d x} (- 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}})

使用微分加减法定则:

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

= - \frac{d}{d x} (7 x^{\frac{4}{3}}) + \frac{d}{d x} (\frac{4}{x ^{3}})

\frac{d}{d x} (7 x^{\frac{4}{3}}) = \frac{28 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

= - \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}}

化简

- \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}} : \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

= \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

y^{2} = 4 x

l in e y = 3 x - 5

s l o p e (0, - 3), (1, - 2)

p o l a r (- 1, 3)

s l o p e x = 5