derivative of-2/((2x+3^2))

解答

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

\frac{8}{( 2 x + 3 ) ^{3}}

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

\frac{d}{d x} (2 x + 3) = 2

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

化简

- 2 (- \frac{2}{( 2 x + 3 ) ^{3}} \cdot 2) : \frac{8}{( 2 x + 3 ) ^{3}}

= \frac{8}{( 2 x + 3 ) ^{3}}

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