If f(x) = lnx / (x+2) what is f'(1) ?

f(x) = lnx/(x+2)

We need to find
the values of f'(1)

First we will need to find the first derivative
f'(x).

Let f(x) = u/v such that:

u= ln
x ==> u' = 1/x

v= x+2 ==> v' =
1

==> f'(x) = u'v-uv' /
v^2

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

==> f'(x) = (x+2)/x - ln x] /
(x+2)^2

==> Now we will substitute with x =
1

==> f'(1) = (1+2)/1 - ln 1] /
(1+2)^2

= (3 - 0) / 9 = 3/9 =
1/3

==> f'(1)=
1/3