The notation

`y = x(ln^3 x)`

means

`y = x(ln x)^3`

Note that we cannot use the log law

`log a^n= n log a`

Our expression is not

`y = x\ ln x^3`

The brackets make all the difference!

This is a product of x and `(ln x)^3`. So

`{: ((dy)/(dx),=x(3(ln x)^2)/x+(ln x)^3(1)),(,=3(ln x)^2+(ln x)^3),(,=(ln x)^2(3+ln x)) :}`