derivative 3/5 x^{5/3}-3/4 x^{1/3}+9

解答

导数

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 9

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

求解步骤

\frac{d}{d x} (\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 9)

化简

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 9 : \frac{3 x ^{\frac{5}{3}}}{5} - \frac{3 x ^{\frac{1}{3}}}{4} + 9

= \frac{d}{d x} (\frac{3 x ^{\frac{5}{3}}}{5} - \frac{3 x ^{\frac{1}{3}}}{4} + 9)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{3 x ^{\frac{5}{3}}}{5}) - \frac{d}{d x} (\frac{3 x ^{\frac{1}{3}}}{4}) + \frac{d}{d x} (9)

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

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

\frac{d}{d x} (9) = 0

= x^{\frac{2}{3}} - \frac{1}{4 x ^{\frac{2}{3}}} + 0

化简

x^{\frac{2}{3}} - \frac{1}{4 x ^{\frac{2}{3}}} + 0 : \frac{- 1 + 4 x ^{\frac{4}{3}}}{4 x ^{\frac{2}{3}}}

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

x \to - 2 + lim (\frac{1 - x}{x ^{3} + 8})

x \to 1 - lim (\frac{2}{x - 1})

\frac{\partial}{\partial x} ((3 x^{2} + y) e^{x y^{2}})

l a pl a ce t r an s f or m (e^{2 t} - e^{t} + t)^{2}

d er i v a t i v e 2 x^{2} - 7 x - 195