derivative of 7x^{-6}-5x^{-3}

解答

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

- \frac{42}{x ^{7}} + \frac{15}{x ^{4}}

求解步骤

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

使用微分加减法定则:

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

= \frac{d}{d x} (7 x^{- 6}) - \frac{d}{d x} (5 x^{- 3})

\frac{d}{d x} (7 x^{- 6}) = - \frac{42}{x ^{7}}

\frac{d}{d x} (5 x^{- 3}) = - \frac{15}{x ^{4}}

= - \frac{42}{x ^{7}} - (- \frac{15}{x ^{4}})

化简

= - \frac{42}{x ^{7}} + \frac{15}{x ^{4}}

d er i v a t i v e y = - 10

36 y^{^{''}} + 36 y^{^{'}} + 11 y = 0, y (0) = 6, y^{^{'}} (0) = 5

t an g e n t \frac{6}{3 x + 1}, at a = - 1

\int (cos (x) + \frac{1}{8} x) d x

x \to 3 - lim (e^{\frac{2}{3 - x}})