What is the differentiation of $log x^2$ ?

Solution :

We have y = $log x^2$

let u = $x^2$ $\implies$ $du\over dx$ = 2x

And, y = log u $\implies$ $dy\over du$ = $1\over u$ = $1\over x^2$

Now, $dy\over dx$ = $dy\over du$ $\times$ $du\over dx$

$\implies$ $dy\over dx$ = $1\over u$ . $du\over dx$

$\implies$ $dy\over dx$ = $1\over x^2$ .2x = $2\over x$

Hence, differentiation of $log x^2$ with respect to x is $2\over x$ .