Solve f''(t) for Vector-Valued Function f(t)

[kcvch]

Question:

If f is a vector-valued function defined by f(t)=(e^(-t), cos(t)), find f''(t).
I'm not even quite sure how to start.

Any help would be loved! Thank you!

 

[kcvch]

Ok, let me clarify. I attempted to take the derivative of each separate part (thus, e^-t became -e^(-t) and so on), but I don't know what to do with it.

 

[rocomath]

What is the difference between ...

$$f'(t)$$ vs $$f''(t)$$ ?

Also, $$x=e^{-t}$$ and $$y=\cos t$$

$$v(t)=<x=f(t),y=f(t),z=f(t)>$$

You can take the derivative of each separately.