What is the derivative of $ln(x^3)$ ?

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Answer 1 · 2015-05-25T19:08:26

We can use the chain rule here, which states that

$(dy)/(dx)=(dy)/(du)(du)/(dx)$

Thus, as it's not possible to directly derivate $ln(x^3)$ , we can rename $u=x^3$ and proceed to derivate $ln(u)$ following chain rule's steps.

$(dy)/(du)=1/u$
and
$(du)/(dx)=3x^2$

Now, aggregating both parts, as stated by the chain rule:

$(dy)/(dx)=1/u*3x^2=1/x^cancel(3)*3cancel(x^2)=color(green)(3/x)$

What is the derivative of ln(x^3)ln(x^3)?