How do you differentiate $[(e^x)(lnx)]/x$ ?

Question

3551 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-19T14:23:39

$e^x/x^2(1+(x-1)lnx)$

$f(x) = (e^xlnx)/x$

$f'(x) = (x(e^x*1/x+e^xlnx)-e^xlnx*1)/x^2$
(Quotient rule and Produce rule)

$f'(x) = (e^x+xe^xlnx-e^xlnx)/x^2$

$= e^x/x^2(1+(x-1)lnx)$

How do you differentiate [(e^x)(lnx)]/x [(e^x)(lnx)]/x ?