derivative f(x)=(6x^2-x+7)^{-5/3}

解答

导数

f (x) = (6 x^{2} - x + 7)^{- \frac{5}{3}}

- \frac{5 ( 12 x - 1 )}{3 ( 6 x ^{2} - x + 7 ) ^{\frac{8}{3}}}

求解步骤

\frac{d}{d x} ((6 x^{2} - x + 7)^{- \frac{5}{3}})

使用连锁律:

- \frac{5}{3 ( 6 x ^{2} - x + 7 ) ^{\frac{8}{3}}} \frac{d}{d x} (6 x^{2} - x + 7)

= - \frac{5}{3 ( 6 x ^{2} - x + 7 ) ^{\frac{8}{3}}} \frac{d}{d x} (6 x^{2} - x + 7)

\frac{d}{d x} (6 x^{2} - x + 7) = 12 x - 1

= - \frac{5}{3 ( 6 x ^{2} - x + 7 ) ^{\frac{8}{3}}} (12 x - 1)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{5 ( 12 x - 1 )}{3 ( 6 x ^{2} - x + 7 ) ^{\frac{8}{3}}}

\frac{d y}{d t} = k (y - 60)

\int \frac{x}{( 4 x + 5 ) ^{2}} d x

x \to 1 lim ((x^{3} + 2) (3 - x))

x \to 3 lim (\frac{( 4 x ^{2} + 3 x )}{5})

in v erse l a pl a ce \frac{10}{2 s + 10}