Question

How do you differentiate $y=\log x^2$?

Answer 1

Compute the required value.

We know that, $\log \left(x^n\right)=n\log \left(x\right)$

So, $\log \left(x^2\right)=2\log \left(x\right)$

Since, $\frac{d}{dx}\log \left(x\right)=\frac{1}{x}$
Thus,

$\frac{d}{dx}2\log \left(x\right)=\frac{2}{x}$

Hence $\frac{dy}{dx}=\frac{d}{dx}\log \left(x^2\right)=\frac{2}{x}$