derivative (3x^2-10)^{-14}

解答

导数

(3 x^{2} - 10)^{- 14}

- \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

求解步骤

\frac{d}{d x} ((3 x^{2} - 10)^{- 14})

使用连锁律:

- \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \frac{d}{d x} (3 x^{2} - 10)

= - \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \frac{d}{d x} (3 x^{2} - 10)

\frac{d}{d x} (3 x^{2} - 10) = 6 x

= - \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \cdot 6 x

化简

- \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \cdot 6 x : - \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

= - \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

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

\int \frac{( 1 )}{( sin ( x ) - 2 csc ( x ) )} d x

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