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

## Solution :

We have y = $$log x^2$$

By using chain rule in differentiation,

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 $$2\over x$$.

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