find the second derivative of the function?

Question

f(t) tsint

Answer 1

well first you have to get the first derivative

so: the 1st derivative= t*cost+1*sint
= cost^2+sint
then you take the derivative of that
so: the 2nd derivative= 2cost*-sint+cost
= -2sintcost+cost

Answer 2

The second derivative is the derivative of the derivative.

Answer 3

You must use the product rule:

f´(t) = 1*sin(t) + t*cost = sin(t) + t*cos(t)

And again:

f´´(t) = cos(t) + 1*cos(t) + t*(-sin(t)) = 2cos(t) - t*sin(t)