
#1
Oct605, 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?




#2
Oct605, 12:26 PM

HW Helper
PF Gold
P: 1,198

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. 



#3
Oct605, 12:50 PM

P: 355

Ah, yes, thanks siddharth!



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