`log_(x)a`.

A

`(-loga)/(a(logx)^(2))`

B

`(-logx)/(x(loga)^(2))`

C

`(loga)/(x(logx)^(2))`

D

`(-loga)/(x(logx)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `y=log_(x)a=(loga)/(logx)`
`therefore (dy)/(dx)=(d)/(dx)((loga)/(logx))`
`=(loga).(d)/(dx)(logx)^(-1)=(loga)(-1)(logx)^(-2).(d)/(dx)(logx)`
`=(-loga)/((logx)^(2))xx(1)/(x)=(-loga)/(x(logx)^(2))`
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