derivative 7(4x^2-7x+2)^{-6}

解答

导数

7 (4 x^{2} - 7 x + 2)^{- 6}

- \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

求解步骤

\frac{d}{d x} (7 (4 x^{2} - 7 x + 2)^{- 6})

将常数提出:

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

= 7 \frac{d}{d x} ((4 x^{2} - 7 x + 2)^{- 6})

使用连锁律:

- \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} \frac{d}{d x} (4 x^{2} - 7 x + 2)

= - \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} \frac{d}{d x} (4 x^{2} - 7 x + 2)

\frac{d}{d x} (4 x^{2} - 7 x + 2) = 8 x - 7

= 7 (- \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} (8 x - 7))

化简

7 (- \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} (8 x - 7)) : - \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

= - \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

x \to \infty lim (x^{2} + 5)

x \to 2 - lim (\frac{x - 1}{x - 2})

x \to \frac{π}{2} lim (cos^{c o s (x)} (x))

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

t an g e n t \frac{( x + 1 )}{( x + 7 )}