How do I do this particle question? (derivatives)

Hi, can someone help me with this?

A particle moves according to a law of motion s = f(t), t>0, where t is seconds and s is feet

for $\displaystyle f(t) = te^{-t/2}$,

a. Find the velocity at time t

so I know to find the derivative, which I got:

$\displaystyle te^{-t/2}(-\frac{1}{2}lnte + \frac{e}{te})$

^pretty sure that's wrong.. can anyone help me with that?

b. When is the particle at rest?

c. When is the particle moving in the positive direction?

d. What is the total distance traveled in the first 8s?

e. Find the acceleration at time t after 3s

f. When is it speeding up? When is it slowing down?

How do I do these as well? With the function I'm using, I am pretty clueless.

Thanks!