I'm trying do it using log differentiation but I'm not really sure how to use log rules to bring down the sqrt (x) . Can I do ln y = sqrt(x) ln cos x ? It seems like I'm wrongly taking the sqrt (x) out of the bracket if I do that?

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- Aug 3rd 2009, 05:22 PMpotatoesNeed derivative of y = cos (x^sqrt(x))
I'm trying do it using log differentiation but I'm not really sure how to use log rules to bring down the sqrt (x) . Can I do ln y = sqrt(x) ln cos x ? It seems like I'm wrongly taking the sqrt (x) out of the bracket if I do that?

- Aug 3rd 2009, 05:28 PMskeeter
- Aug 3rd 2009, 05:41 PMpotatoes
Ok thanks.

So that gives me dy/dx = -sin u * (sqrt(x)lnx + 2sqrt(x)/2x) * u

At this point does the derivative become dy/du? and then I can just leave it like that? or do I sub in x^sqrt(x) for u? - Aug 3rd 2009, 05:50 PMskeeter

finally ...

- Aug 3rd 2009, 05:52 PMpotatoes
Ok great. Thanks so much.