derivative 3/(x-4)

解答

导数

\frac{3}{x - 4}

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

求解步骤

\frac{d}{d x} (\frac{3}{x - 4})

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

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