derivative f(x)=(11)/((1-x)^2)

解答

导数

f (x) = \frac{11}{( 1 - x ) ^{2}}

\frac{22}{( 1 - x ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{11}{( 1 - x ) ^{2}})

将常数提出:

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

= 11 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{2}})

使用指数法则:

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

= 11 \frac{d}{d x} ((1 - x)^{- 2})

使用连锁律:

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

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

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

= 11 (- \frac{2}{( 1 - x ) ^{3}} (- 1))

化简

11 (- \frac{2}{( 1 - x ) ^{3}} (- 1)) : \frac{22}{( 1 - x ) ^{3}}

= \frac{22}{( 1 - x ) ^{3}}

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