derivative 1/((2x+1)^2)

解答

导数

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

- \frac{4}{( 2 x + 1 ) ^{3}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

- \frac{2}{( 2 x + 1 ) ^{3}} \frac{d}{d x} (2 x + 1)

= - \frac{2}{( 2 x + 1 ) ^{3}} \frac{d}{d x} (2 x + 1)

\frac{d}{d x} (2 x + 1) = 2

= - \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2

化简

- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2 : - \frac{4}{( 2 x + 1 ) ^{3}}

= - \frac{4}{( 2 x + 1 ) ^{3}}

\int \frac{1}{x ^{2} 4 x ^{2} - 25} d x

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\int e^{0.04 x} d x