derivative of (4x^2-13^{-14})

解答

\frac{d}{d x} ((4 x^{2} - 13)^{- 14})

- \frac{112 x}{( 4 x ^{2} - 13 ) ^{15}}

求解步骤

\frac{d}{d x} ((4 x^{2} - 13)^{- 14})

使用连锁律:

- \frac{14}{( 4 x ^{2} - 13 ) ^{15}} \frac{d}{d x} (4 x^{2} - 13)

= - \frac{14}{( 4 x ^{2} - 13 ) ^{15}} \frac{d}{d x} (4 x^{2} - 13)

\frac{d}{d x} (4 x^{2} - 13) = 8 x

= - \frac{14}{( 4 x ^{2} - 13 ) ^{15}} \cdot 8 x

化简

- \frac{14}{( 4 x ^{2} - 13 ) ^{15}} \cdot 8 x : - \frac{112 x}{( 4 x ^{2} - 13 ) ^{15}}

= - \frac{112 x}{( 4 x ^{2} - 13 ) ^{15}}

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