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

解答

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

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

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

= 2 ((1 + x)^{- 3})^{^{'}}

使用连锁律:

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

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

(1 + x)^{'} = 1

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

化简

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

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

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