derivative of (3x^2-9^{-14})

解

\frac{d}{d x} ((3 x^{2} - 9)^{- 14})

- \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}

解答ステップ

\frac{d}{d x} ((3 x^{2} - 9)^{- 14})

連鎖法則を適用:

- \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \frac{d}{d x} (3 x^{2} - 9)

\frac{d}{d x} (3 x^{2} - 9) = 6 x

= - \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \cdot 6 x

簡素化

- \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \cdot 6 x : - \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}

= - \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}