derivative of 4/((x^2+9^3))

解答

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

- \frac{24 x}{( x ^{2} + 9 ) ^{4}}

求解步骤

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

将常数提出:

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

= 4 \frac{d}{d x} (\frac{1}{( x ^{2} + 9 ) ^{3}})

使用指数法则:

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

= 4 \frac{d}{d x} ((x^{2} + 9)^{- 3})

使用连锁律:

- \frac{3}{( x ^{2} + 9 ) ^{4}} \frac{d}{d x} (x^{2} + 9)

= - \frac{3}{( x ^{2} + 9 ) ^{4}} \frac{d}{d x} (x^{2} + 9)

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

= 4 (- \frac{3}{( x ^{2} + 9 ) ^{4}} \cdot 2 x)

化简

4 (- \frac{3}{( x ^{2} + 9 ) ^{4}} \cdot 2 x) : - \frac{24 x}{( x ^{2} + 9 ) ^{4}}

= - \frac{24 x}{( x ^{2} + 9 ) ^{4}}

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