Given:
[tex]y=\log_{\sqrt{x}}x[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=\log_{\sqrt{x}}x[/tex]
It can be written as
[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]
Using property of log, we get
[tex]y=2[/tex] [tex][\because \log_aa^x=x][/tex]
Now, differentiate both sides with respect to x.
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]
[tex]\dfrac{dy}{dx}=0[/tex] [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.
