derivative of 2/(9+x^2)

解答

\frac{d}{d x} (\frac{2}{9 + x ^{2}})

- \frac{4 x}{( 9 + x ^{2} ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{2}{9 + x ^{2}})

将常数提出:

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

= 2 \frac{d}{d x} (\frac{1}{9 + x ^{2}})

使用指数法则:

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

= 2 \frac{d}{d x} ((9 + x^{2})^{- 1})

使用连锁律:

- \frac{1}{( 9 + x ^{2} ) ^{2}} \frac{d}{d x} (9 + x^{2})

= - \frac{1}{( 9 + x ^{2} ) ^{2}} \frac{d}{d x} (9 + x^{2})

\frac{d}{d x} (9 + x^{2}) = 2 x

= 2 (- \frac{1}{( 9 + x ^{2} ) ^{2}} \cdot 2 x)

化简

2 (- \frac{1}{( 9 + x ^{2} ) ^{2}} \cdot 2 x) : - \frac{4 x}{( 9 + x ^{2} ) ^{2}}

= - \frac{4 x}{( 9 + x ^{2} ) ^{2}}

\frac{d}{d x} (e^{2} (2 x + 4))

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