How do you differentiate #f(x)=xe^(1-sqrt(x)ln(x))#?

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Answer 1 · 2015-10-11T10:52:12

#f'(x)=e^(1-sqrtx lnx)(1-1/2sqrtxlnx-sqrtx)#

#f(x)=xe^(1-sqrtx lnx)#

#f'(x)=e^(1-sqrtx lnx)+xe^(1-sqrtx lnx)(-(1/(2sqrtx)lnx+sqrtx1/x))#

#f'(x)=e^(1-sqrtx lnx)-xe^(1-sqrtx lnx)(1/(2sqrtx)lnx+1/sqrtx)#

#f'(x)=e^(1-sqrtx lnx)-xe^(1-sqrtx lnx)((lnx+2)/(2sqrtx))#

#f'(x)=e^(1-sqrtx lnx)-e^(1-sqrtx lnx)((sqrtxlnx-2sqrtx)/2)#

#f'(x)=e^(1-sqrtx lnx)(1-1/2sqrtxlnx-sqrtx)#

How do you differentiate #f(x)=x*e^(1-sqrt(x)*ln(x))#?