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The derivative of log|x| is...

The derivative of log|x| is

A

`(1)/(x), x gt 0`

B

`(1)/(|x|), x ne 0`

C

`(1)/(x), x ne 0`

D

None of these

Text Solution

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The correct Answer is:
C
We have `y=log|x|={{:(,log x,x gt0),(,log(-x),x lt ):}`
`therefore (dy)/(dx)={{:(,(1)/(x), x gt0),(,(1)/(-x)(-1)=(1)/(x),x lt 0):}`
`Rightarrow (dy)/(dx)=(1)/(x), x ne 0`
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