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

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Answer 1 · 2016-07-24T03:51:50

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

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

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

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