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 \(2\over x\).