Question

Y=log base(rootx) x find dy/dx

Answer 1

Given:

`y=\log_(√(x))x`

To find:

The value of
`(dy)/(dx)`.

Solution:

We have,

`y=\log_(√(x))x`

It can be written as

`y=\log_(√(x))(√(x))^2`

Using property of log, we get

`y=2`
`[\because \log_aa^x=x]`

Now, differentiate both sides with respect to x.

`(dy)/(dx)=(d)/(dx)(2)`

`(dy)/(dx)=0`
`[\because (d)/(dx)(Constant)=0]`

Therefore, the value of
`(dy)/(dx)` is 0.