How do you differentiate $f(x)=x^(ln x)$ ?

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Answer 1 · 2015-11-02T19:14:09

See the explanation section, below.

$y=x^(lnx)$ $rArr$ $lny = lnx^(lnx) = lnx lnx = (lnx)^2$

Differentiate implicitely:

$1/y dy/dx = 2(lnx)* 1/x$

So, $dy/dx = y(2lnx)/x = (2lnx)/x x^(lnx)$

How do you differentiate f(x)=x^(ln x)f(x)=x^(ln x)?