What is the instantaneous velocity of an object moving in accordance to # f(t)= (t^3-t^2-3,e^(2t)) # at # t=6 #? Calculus Derivatives Instantaneous Velocity 1 Answer turksvids Dec 23, 2017 #f'(6)=(96,2e^12)# Explanation: Find #f'(t)# component-by-component: #f'(t)=(d/dt(t^3-t^2-3),d/dt(e^(2t)))# #f'(t)=(3t^2-2t,2e^(2t))# Find #f'(6)# by direct substitution: #f'(6)=(3(36)-12,2e^12) = (96,2e^12)# Answer link Related questions What is Instantaneous Velocity? How do you find the instantaneous velocity of a curve? How do you find the instantaneous velocity at #t=0# for the position function #s(t) = 6t^2 +8t#? How do you find the instantaneous velocity at #t=2# for the position function #s(t) = t^3 +8t^2-t#? How do you find the instantaneous velocity of the particle? How can instantaneous velocity be found from a displacement-time graph? How do you find instantaneous velocity in calculus? How does instantaneous velocity differ from average velocity? What is the difference between instantaneous velocity and speed? What represents instantaneous velocity on a graph? See all questions in Instantaneous Velocity Impact of this question 1805 views around the world You can reuse this answer Creative Commons License