derivative of-1/5 (x^{-5}-x^{10})

解答

\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

\frac{2 x ^{15} + 1}{x ^{6}}

求解步骤

\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

将常数提出:

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

= - \frac{1}{5} \frac{d}{d x} (x^{- 5} - x^{10})

使用微分加减法定则:

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

= - \frac{1}{5} (\frac{d}{d x} (x^{- 5}) - \frac{d}{d x} (x^{10}))

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

\frac{d}{d x} (x^{10}) = 10 x^{9}

= - \frac{1}{5} (- \frac{5}{x ^{6}} - 10 x^{9})

化简

- \frac{1}{5} (- \frac{5}{x ^{6}} - 10 x^{9}) : \frac{2 x ^{15} + 1}{x ^{6}}

= \frac{2 x ^{15} + 1}{x ^{6}}

\frac{\partial}{\partial v} (u \cdot sin (v))

d er i v a t i v e f (x) = ∣ x - 2 ∣

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

t an g e n t f (x) = 5 - x^{2}, at x = 1

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