derivative of 3sqrt(x)+2/(5x^3-sqrt(2))

解答

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

\frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

求解步骤

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

化简

3 x + \frac{2}{5 x ^{3}} - 2 : - 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}

= \frac{d}{d x} (- 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

使用微分加减法定则:

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

= - \frac{d}{d x} (2) + \frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}) = \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

= - 0 + \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

化简

= \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

x (\frac{d y}{d x}) - 3 y = x^{3}, y (1) = 1

\frac{d y}{d x} = \frac{y}{x} - \frac{x ^{2}}{y ^{2}}

x \to 0 + lim (\frac{ln ( x )}{x ^{2}})

\frac{d y}{d t} = 5 y + y^{5}

d er i v a t i v e x - \frac{1}{3 x ^{3}}