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

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Answer 1 · 2015-03-01T15:29:03

The answer is: $y'=2e^(2xlnx)(lnx+1)$ .

Instead of remembering a complicate formula, we use these logarithmic properties:

$a=e^lna$ or, better: $a^b=e^ln(a^b)=e^(blna)$ .

So our function becomes:

$y=e^(2xlnx)$

and

$y'=e^(2xlnx)(2*1*lnx+2x*1/x)=2e^(2xlnx)(lnx+1)$ .

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