f(x) = x^2 -3 ln x fin f'(1)

We'll calculate the expression of  f'(x)
first:

f'(x) = (x^2 -3 ln
x)'  

f'(x) = 2x - 3/x

We'll
substitute x by 1 and we'll get:

f'(1) = 2*1 -
3/1

f'(1) = 2 -
3

f'(1) =
-1

Another method is to
calculate the limit of the
ratio:

lim [f(x) -
f(1)/(x-1)],when x->1