derivative of-1/3 (x^{-3}-x^6)

解答

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

\frac{2 x ^{9} + 1}{x ^{4}}

求解步骤

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{3} \frac{d}{d x} (x^{- 3} - x^{6})

使用微分加减法定则:

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

= - \frac{1}{3} (\frac{d}{d x} (x^{- 3}) - \frac{d}{d x} (x^{6}))

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= - \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5})

化简

- \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5}) : \frac{2 x ^{9} + 1}{x ^{4}}

= \frac{2 x ^{9} + 1}{x ^{4}}

\frac{\partial}{\partial x} (x cos (x y) - 2 y)

\frac{d}{d x} (cos (x) sec^{7} (x))

\int 3 sin^{3} (x co) s^{2} x d x

x \to 1 lim (\frac{2 x - 5}{x + 1})

\frac{d}{d x} (\frac{k x + a}{b x + c})