How do you differentiate $f (x) = x \cdot e^{1 - \sqrt{x} \cdot ln (x)}$ $f(x)=xe^(1-sqrt(x)ln(x))$ ?

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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))f(x)=x⋅e1−√x⋅ln(x)f(x)=x*e^(1-sqrt(x)*ln(x))?