Find an equation for the tangent line to the curve y=(e^x)/(1+lnx) at the point where x=1.

Can someone check my work please?

y=e^x/(1+lnx)

y'=[e^x(1+lnx)-e^x(1/x)]/(1+lnx)^2

f'(1)=e(0)/1

=0

y=mx+b

e=0(1)+b

e=b

therefore the equation of the tangent is

y=e

Is this correct? thank you in advance!