Find the first and second derivative of $(2lnx)/x$ ?

Question

4885 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-10T20:34:09

$f'(x) \ = (2lnx)/x$

$f''(x) = (2-2lnx)/(x^2)$

We have:

$f(x) = ln^2x$

Differentiating once (using the chain rule) we get:

$f'(x) = (2lnx )(d/d ln x )$
$" " = (2lnx )(1/x)$
$" " = (2lnx)/x$

Ti get the second derivative we apply the quotient rule:

$f''(x) = ((x)(d/dx2lnx)-(2lnx)(d/dxx))/(x^2)$
$" " = ((x)(2/x)-(2lnx)(1))/(x^2)$
$" " = (2-2lnx)/(x^2)$

Find the first and second derivative of (2lnx)/x(2lnx)/x?