Compute the higher order derivative :

Question

f(t) =tcost, find the f ' ' ' ( 0 ),

 

thanks!!

Answer 1

f(t) = tcos(t)

 

To find the third derivative, apply the Product Rule each time:

 

f '(t) = cos(t) - tsin(t)

 

f ''(t) = -sin(t) - sin(t) - tcos(t) = -2sin(t) - tcos(t)

 

f '''(t) = -2cos(t) - cos(t) + tsin(t) = -3cos(t) + tsin(t)

 

Evaluate f ''' at t=0:

 

f '''(0) = -3cos(0) + (0)sin(0) = -3