Math Is Fun Forum

bossk171

Member

Registered: 2007-07-16

Posts: 305

derivative of x^x

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Ahhhhhh, I went here: http://calc101.com/webMathematica/deriv … sp#topdoit To try to figure it out, but I don't get it.

Usually I don't get stuck with calc, but I really don't get their explanation.

Can you guys give me a step by step on this one, this just doesn't make sense.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: derivative of x^x

Not a bad site, but the problem is that an algorithm is not going to give you the easiest way to take the derivative.

y = x^x

ln(y) = ln(x^x) = x*ln(x)

d/dy ln(y) = d/dx x*ln(x)

1/y*dy = x*1/x + ln(x)*1

dy = y(1 + ln(x))

dy = x^x(1 + ln(x))

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: derivative of x^x

Nice, thanks.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Krizalid

Member

Registered: 2007-03-09

Posts: 51

Re: derivative of x^x

Another faster way it is to set

, then we get the derivative quickly.