derivative of-4/((1+2x^2))

解答

\frac{d}{d x} (- \frac{4}{( 1 + 2 x ) ^{2}})

\frac{16}{( 1 + 2 x ) ^{3}}

求解步骤

\frac{d}{d x} (- \frac{4}{( 1 + 2 x ) ^{2}})

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

= - 4 (- \frac{2}{( 1 + 2 x ) ^{3}} \cdot 2)

化简

- 4 (- \frac{2}{( 1 + 2 x ) ^{3}} \cdot 2) : \frac{16}{( 1 + 2 x ) ^{3}}

= \frac{16}{( 1 + 2 x ) ^{3}}

\frac{d}{d x} (\frac{3}{4 x})

\int_{0}^{\frac{π}{4}} 8 sec^{2} (x) d x

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