derivative f(x)=-1/9 (x^{-9}-x^{18})

解答

导数

f (x) = - \frac{1}{9} (x^{- 9} - x^{18})

\frac{2 x ^{27} + 1}{x ^{10}}

求解步骤

\frac{d}{d x} (- \frac{1}{9} (x^{- 9} - x^{18}))

将常数提出:

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

= - \frac{1}{9} \frac{d}{d x} (x^{- 9} - x^{18})

使用微分加减法定则:

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

= - \frac{1}{9} (\frac{d}{d x} (x^{- 9}) - \frac{d}{d x} (x^{18}))

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

\frac{d}{d x} (x^{18}) = 18 x^{17}

= - \frac{1}{9} (- \frac{9}{x ^{10}} - 18 x^{17})

化简

- \frac{1}{9} (- \frac{9}{x ^{10}} - 18 x^{17}) : \frac{2 x ^{27} + 1}{x ^{10}}

= \frac{2 x ^{27} + 1}{x ^{10}}

\int \frac{1}{16 e ^{- 5 x} + e ^{5 x}} d x

t an g e n t (4 - x) y^{2} = x^{3}, (2, 2)

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

\int 4 x^{7} d x

d er i v a t i v e f (x) = 0.0622 x^{2} + 1.1119 x + 2.3979