The derivative of log|x| is

Options

A. `(1)/(x),x gt 0`
B. `(1)/(|x|),xne0`
C. `(1)/(x),xne0`
D. none of these

Answer

C

Explanation

We wave,
`y=log|x|={{:(logx,xgt0),(log(-x),xlt0):}`
`therefore(dy)/(dx)={{:((1)/(x),x gt 0),((1)/(-x)(-1)=(1)/(x),x lt 0):}`
`implies(dy)/(dx)=(1)/(x),xne0`