How do you find the derivative of $x^(2 lnx)$ ?

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Answer 1 · 2018-04-15T12:07:29

$y'=4x^(2lnx)lnx/x$

$y=x^(2lnx)$

by taking the natural logarithm to both sides

$lny=lnx^(2lnx)$

using the properties of the logarithmic functions
$color(green) (lnu^v=vlnu)$

$lny=2lnx*lnx$

$lny$ = $2(lnx)^2$

Differentiate

$(y')/y=4lnx/x$

$y'=4ylnx/x$

Substitute for $y$

$y'=4x^(2lnx)lnx/x$

How do you find the derivative of x^(2 lnx)x^(2 lnx)?