ddx13x+2=−12(3x+2)32.ddx(3x+2)=−321(3x+2)32=−32(3x+2)32

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

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

$\frac{- 3}{2 {(3 x - 2)}^{\frac{3}{2}}}$

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

$\frac{3}{2 {(3 x - 2)}^{\frac{3}{2}}}$

answer is B.

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Detailed Solution

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

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

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