derivative of 1/(sqrt(2x+3))

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

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