Your f'(t) is not correct.

f(t) = P(1 + r/m)^mt

What are variables here?

Only f(t) and t.

The P, r and m are all constants ---they don't change in the given f(t).

So the function is in the form

f(t) = P[(a)^(g(t))]

d/dx a^u = ln(a) *a^u *du/dx --------------***

Hence,

f(t) = P(1 + r/m)^mt

f'(t) = P[ln(1 +r/m)]*[(1 +r/m)^mt]*m -----(i)

Given:

P = $10,000

r = 4% per annum = 0.04

m = 2 ----semi-annualy

t = 3 years

Plug those into (i),

f'(t) = ($10,000)[ln(1 +0.04/2)]*[(1 +0.04/2)^(2*3)]*2

f'(t) = $446.02