derivative of (2x^2-6x+1^{-8})

解

\frac{d}{d x} ((2 x^{2} - 6 x + 1)^{- 8})

- \frac{8 ( 4 x - 6 )}{( 2 x ^{2} - 6 x + 1 ) ^{9}}

解答ステップ

\frac{d}{d x} ((2 x^{2} - 6 x + 1)^{- 8})

連鎖法則を適用:

- \frac{8}{( 2 x ^{2} - 6 x + 1 ) ^{9}} \frac{d}{d x} (2 x^{2} - 6 x + 1)

= - \frac{8}{( 2 x ^{2} - 6 x + 1 ) ^{9}} \frac{d}{d x} (2 x^{2} - 6 x + 1)

\frac{d}{d x} (2 x^{2} - 6 x + 1) = 4 x - 6

= - \frac{8}{( 2 x ^{2} - 6 x + 1 ) ^{9}} (4 x - 6)

分数を乗じる:

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

= - \frac{8 ( 4 x - 6 )}{( 2 x ^{2} - 6 x + 1 ) ^{9}}