derivative f(x)=-1/6 (x^{-6}+x^{12})

解答

导数

f (x) = - \frac{1}{6} (x^{- 6} + x^{12})

- \frac{- 1 + 2 x ^{18}}{x ^{7}}

求解步骤

\frac{d}{d x} (- \frac{1}{6} (x^{- 6} + x^{12}))

将常数提出:

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

= - \frac{1}{6} \frac{d}{d x} (x^{- 6} + x^{12})

使用微分加减法定则:

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

= - \frac{1}{6} (\frac{d}{d x} (x^{- 6}) + \frac{d}{d x} (x^{12}))

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

\frac{d}{d x} (x^{12}) = 12 x^{11}

= - \frac{1}{6} (- \frac{6}{x ^{7}} + 12 x^{11})

化简

- \frac{1}{6} (- \frac{6}{x ^{7}} + 12 x^{11}) : - \frac{- 1 + 2 x ^{18}}{x ^{7}}

= - \frac{- 1 + 2 x ^{18}}{x ^{7}}