# Math Help - What is f'(e) for f(x) = x/(lnx)

1. ## What is f'(e) for f(x) = x/(lnx)

I said, using the quotient rule,

f'(x)[1(lnx) - x(1/x)]/(lnx)^2 = lnx - 1

so f'(e) = (lne - 1) / (lne)^2 = 1-1/1 = 0/1 = 0

2. Originally Posted by satx
I said, using the quotient rule,

f'(x)[1(lnx) - x(1/x)]/(lnx)^2 = lnx - 1 <... ?

so f'(e) = (lne - 1) / (lne)^2 = 1-1/1 = 0/1 = 0
so $f'(x)=\frac{\log(x)-1}{\log^2(x)}$
which means $f'(e)=\frac{\log(e)-1}{\log^2(e)}=0$
you're right