I can't figure out where I erred in calculating this derivative:
$f(t) = 4.9t^2$
f'(t) = \frac {f(t+h) - f(t)} {h} = \frac {4.9(t+h)^2 - 4.9t^2} {h} $= \frac {4.9(t^2 + h^2 +2ht) - 4.9t^2} {h} = \frac {4.9t^2 + 4.9h ^2 + 9.8ht - 4.9t^2} { h}$ $=\frac {4.9h^2 + 9.8ht} { h} = 4.9h+9.8t$
Obviously the correct answer is $9.8t$. I think my fault was in the last step, for some reason I'm still a bit confused when it comes to dividing the difference by $h$.