Question

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

Answer 1

Given:

$y=\log_{\sqrt{x}}x$

To find:

The value of $\dfrac{dy}{dx}$.

Solution:

We have,

$y=\log_{\sqrt{x}}x$

It can be written as

$y=\log_{\sqrt{x}}(\sqrt{x})^2$

Using property of log, we get

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

Now, differentiate both sides with respect to x.

$\dfrac{dy}{dx}=\dfrac{d}{dx}(2)$

$\dfrac{dy}{dx}=0$          $[\because \dfrac{d}{dx}(Constant)=0]$

Therefore, the value of $\dfrac{dy}{dx}$ is 0.