Question

How do I find the derivative of `ln(x^2)`?

Answer 1

Derivative of `lnx^2` is `2/x`

Explanation:

We can use the chain rule for `(df(g(x)))/(dx)=(df)/(dg)xx(dg)/(dx)`

As here we have `f(x)=ln(x^2)`

`(dln(x^2))/(dx)=(dln(x^2))/(d(x^2))xx(dx^2)/(dx)`

= `1/x^2xx2x`

= `2x/x^2`

= `2/x`

Other way could be using formula for log and

`(dln(x^2))/(dx)=(d(2lnx))/(dx)=2(d(lnx))/(dx)=2/x`