derivative of 5/(25x^2+1)

解答

\frac{d}{d x} (\frac{5}{25 x ^{2} + 1})

- \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5}{25 x ^{2} + 1})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{25 x ^{2} + 1})

使用指数法则:

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

= 5 \frac{d}{d x} ((25 x^{2} + 1)^{- 1})

使用连锁律:

- \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (25 x^{2} + 1)

= - \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (25 x^{2} + 1)

\frac{d}{d x} (25 x^{2} + 1) = 50 x

= 5 (- \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \cdot 50 x)

化简

5 (- \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \cdot 50 x) : - \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}}

= - \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}}

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