derivative (5x^9+7x^2-65)^{-9}

解答

导数

(5 x^{9} + 7 x^{2} - 65)^{- 9}

- \frac{9 ( 45 x ^{8} + 14 x )}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}}

求解步骤

\frac{d}{d x} ((5 x^{9} + 7 x^{2} - 65)^{- 9})

使用连锁律:

- \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} \frac{d}{d x} (5 x^{9} + 7 x^{2} - 65)

= - \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} \frac{d}{d x} (5 x^{9} + 7 x^{2} - 65)

\frac{d}{d x} (5 x^{9} + 7 x^{2} - 65) = 45 x^{8} + 14 x

= - \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} (45 x^{8} + 14 x)

分式相乘:

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

= - \frac{9 ( 45 x ^{8} + 14 x )}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}}

d er i v a t i v e \frac{100}{x ^{2}}

d er i v a t i v e 5 t^{2} - 2 t

d er i v a t i v e (s^{2} + a)^{- 2}

d er i v a t i v e cos (x - 2 5^{\circ})

d er i v a t i v e \frac{x}{( x ^{2} + 1 ) ^{2}}