What is the derivative of $x^(lnx)$ ?

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Answer 1 · 2015-08-09T11:26:05

$d/dxx^(ln x) = 2x^(ln x-1) ln x$

Let $y = x^(ln x)$
Taking the natural logarithm:
$ln y = (ln x)^2$

Taking the derivative with respect to x:
$1/y dy/dx = (2ln x)/x$
$dy/dx = 2x^(ln x-1) ln x$

What is the derivative of x^(lnx)x^(lnx)?