derivative 5/(sqrt(x)+5)

解答

导数

\frac{5}{x + 5}

- \frac{5}{2 x ( x + 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5}{x + 5})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{x + 5})

使用指数法则:

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

= 5 \frac{d}{d x} ((x + 5)^{- 1})

使用连锁律:

- \frac{1}{( x + 5 ) ^{2}} \frac{d}{d x} (x + 5)

= - \frac{1}{( x + 5 ) ^{2}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = \frac{1}{2 x}

= 5 (- \frac{1}{( x + 5 ) ^{2}} \cdot \frac{1}{2 x})

化简

5 (- \frac{1}{( x + 5 ) ^{2}} \cdot \frac{1}{2 x}) : - \frac{5}{2 x ( x + 5 ) ^{2}}

= - \frac{5}{2 x ( x + 5 ) ^{2}}

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