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February 20th, 2009, 07:26 AM   #1
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Chain Rule

y=[e^(u) - e^(-u)] / [e^(u) - e^(-u)]

How do would you treat "u" when differentiating with "e"?
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February 20th, 2009, 09:58 AM   #2
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Re: Chain Rule

One of those subtraction signs wants to be a plus, I think. But anyway...

If you're differentiating with respect to u, then for e^u it's as simple as...



... whereas ...



On the other hand, if u is standing for a function of some other variable, as it often does, and you're differentiating with
respect to that other variable, then apply the chain rule accordingly - e.g.,



Don't integrate - balloontegrate!

http://www.ballooncalculus.org/examples
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