calculus 1
posted by monic .
Differentiate.
f(x) = 8 − x^ex/x + ex
f '(x) =

Hard to tell just what you mean there. If you mean
f(x) = (8xe^x)/(x+e^x)
f' = [(e^x  xe^x)(x+e^x)  (8xe^x)(1+e^x)]/(x+e^x)^2
= (xe^x  x^2 e^x  e^2x  xe^2x  8 + xe^x  8e^x + xe^2x)/(x+e^x)^2
= (e^x(x+x^2e^xxe^x+x8+xe^x)8)/(x+e^x)^2
= (e^x(x^2e^x8)8)/(x+e^x)^2
doesn't get much simpler
If I got the original wrong, fix it and visit wolframalpha.com