What is the derivative of $f(x)= ln2x$ ?

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Answer 1 · 2016-01-15T02:29:31

$f'(x)=1/x$

According to the chain rule,

$d/dx[lnu]=1/u*u'$

Thus,

$d/dx[ln2x]=1/(2x)*d/dx[2x]$

$=1/(2x)*2=1/x$

Another way to think about this problem is to first split up the logarithm using logarithm rules:

$f(x)=ln2+lnx$

Thus, when differentiating, $ln2$ is just a constant, so

$f'(x)=d/dx[lnx]=1/x$

What is the derivative of f(x)= ln2xf(x)= ln2x?