What is the derivative of $ln(2x)$ ?

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Answer 1 · 2016-04-03T09:00:58

$(ln(2x))' = 1/(2x) * 2 = 1/x.$

You use the chain rule :

$(f @ g)'(x) = (f(g(x)))' = f'(g(x)) * g'(x)$ .

In your case : $(f @ g)(x) = ln(2x), f(x) = ln(x) and g(x) = 2x$ .

Since $f'(x) = 1/x and g'(x) = 2$ , we have :

$(f @ g)'(x) = (ln(2x))' = 1/(2x) * 2 = 1/x$ .

Answer 2 · 2016-04-03T09:04:51

$1/x$

You can also think of it as

$ln(2x) = ln(x) + ln(2)$

$ln(2)$ is just a constant so has a derivative of $0$ .

$d/dx ln(x) = 1/x$

Which gives you the final answer.

What is the derivative of ln(2x)ln(2x)?