Question

How do you differentiate `y=ln(3x)`?

Answer 1

`(dy)/(dx)=1/x`

Explanation:

Let `g(x)=3x`, hence `y=y(g(x))`, where `f(x)=lnx`

Now using chain rule, `(dy)/(dx)=(dy)/(dg)xx(dg)/(dx)`

Hence `(dy)/(dx)=1/(3x)xx3=1/x`

Altrnatively

`y=ln(3x)=ln3+lnx` and as `ln3` is a constant term

`(dy)/(dx)=d/(dx)lnx=1/x`