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If y="log"(2)"log"(2)(x), then (dy)/(dx)...

If `y="log"_(2)"log"_(2)(x)`, then `(dy)/(dx)` is equal to

A

`(log_(2)e)/(log_(e)x)`

B

`(log_(2)e)/(x log_(x)2)`

C

`(log_(2)x)/(log_(e)2)`

D

`(log_(2)e)/(x log_(e)x)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `y=log_(2)log_(2)(x)`
`=(log_(e)log_(2)(x))/(log_(e)2)=(log_(e)[(log_(e)x)/(log_(e)2)])/(log_(e)2)`
`impliesy=(log_(e)log_(e)x-log_(e)log_(e)2)/(log_(e)2)`
On differentiating w.r.t. x, we get
`(dy)/(dx)=(1)/(log_(e)2)[(1)/(xlog_(e)x)-0]`
`=(log_(2)e)/(xlog_(e)x)`
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