Differentiating


by TSN79
Tags: differentiating
TSN79
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#1
Oct6-05, 12:10 PM
P: 355
I'm having some trouble differentiating [itex] x^{\sqrt x } [/itex]. I know that the derivative of [itex] x^{\sqrt x } [/itex] probably begins with [itex] x^{\sqrt x } \cdot \ln (x) \cdot \frac{1}{{2\sqrt x }} [/itex] but once the base is also x then there is probably more to it than that. Anyone?
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siddharth
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#2
Oct6-05, 12:26 PM
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You have [tex] y=x^{\sqrt x } [/tex]
So, [tex] \ln y = (\sqrt x)(\ln x) [/tex]
Then differentiate both sides with respect to x and substitute the value of y.
TSN79
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#3
Oct6-05, 12:50 PM
P: 355
Ah, yes, thanks siddharth!


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