What is the instantaneous velocity of an object with position at time t equal to # f(t)= (te^(t^2-3t),t^2-e^t) # at # t=3 #? Calculus Derivatives Instantaneous Velocity 1 Answer Eddie Jun 24, 2016 #(10, 6 - e^3) # Explanation: #f(t)= (te^(t^2-3t),t^2-e^t)# #f'(t)= (e^(t^2-3t) + t (2t-3) e^(t^2-3t),2t-e^t)# #= (e^(t^2-3t) (1 + t (2t-3)),2t-e^t)# #f'(3) = ( (1)(1 + 3(3)), 6 - e^3) = (10, 6 - e^3) # 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 1296 views around the world You can reuse this answer Creative Commons License