Why can't you apply the chain rule to lnx
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Why can't you apply the chain rule to lnx

[From: ] [author: ] [Date: 11-05-04] [Hit: ]
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(x^lnx)' <= Why can't you apply the chain rule here?

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If you can express x^lnx as the composition of two functions then you can apply the chain rule.

The difficulty is that there is no obvious way to express x^lnx as the composition of two functions.

So, you take ln of both sides of the equation y = x^lnx and get

lny = lnx lnx

so

lny = (lnx)^2

Now you do use the chain rule on both the left and right sides:

(1/y)y' = 2lnx 1/x, so

y' = 2y lnx /x

y' = 2(x^lnx)(lnx) / x
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