06-06-2005, 10:59 AM
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#22
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Iron Throne Cult 
Join Date: January 2, 2003
Location: Big Castle in the Sky
Age: 38
Posts: 4,835
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Quote:
Originally posted by Azred:
Seraph, your girlfriend got the right answer and differentiated the function correctly.
Then function is question is an exponential function; in its generic form looks like this: f(x) = k ^ x, with k being a non-negative numbers (usually). The first derivative takes the form f'(x) = (ln k) * (k ^ x). Multiple derivatives have this form: (f(n))(x) = ((ln k)^n) * (k ^ x).
If it helps, you could always think of letting k = e, because finding derivatvies for e^x is really easy. [img]graemlins/beigesmilewinkgrin.gif[/img]
Interestingly, if you let k = sqrt(2), begin with an x-value of 1, and iterate the function (the x-value of the next step is the f(x)-value from the last step) then the iterated function values converge to sqrt(2). [img]graemlins/petard.gif[/img]
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I hate you all now [img]tongue.gif[/img]
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