derivative 2/((x+1)^3)

解答

导数

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

2 (- \frac{3}{( x + 1 ) ^{4}} \cdot 1) : - \frac{6}{( x + 1 ) ^{4}}

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

t an g e n t f (x) = \frac{4 x}{x ^{2} + 1}, (1, 2)

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