Question

evaluate the derivative by using the appropriate Product Rule, where r_1(t) = <t^2, t^3, t>, r_2(t) = <e^{3t}, e^{2t}, e^t> a) d/dt (r_1(t) ? r_2(t)) b) d/dt (r_1(t) % r_2(t))

          evaluate the derivative by using the appropriate Product Rule, where

r_1(t) = <t^2, t^3, t>, r_2(t) = <e^{3t}, e^{2t}, e^t>

a) d/dt (r_1(t) ? r_2(t))

b) d/dt (r_1(t) % r_2(t))

Added by Esperanza C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/19/2023

Step 1

r1(t) x r2(t) = (t^2, 8, t) x (e^{3t}, e^{2t}, e^t) = (8e^t - te^{2t}, te^{3t} - t^2e^t, t^2e^{2t} - 8e^{3t}) Now, we need to find the derivative of the cross product with respect to t. \frac{d}{dt}(r1(t) x r2(t)) = \frac{d}{dt}(8e^t - te^{2t}, te^{3t} - Show more…

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evaluate the derivative by using the appropriate Product Rule, where r1 (t) = (t2,8, ',,t) , I2 (t) = (e3t , e2t, et) dt (1 (t) - r2 ()) d 9 bl d dt (r1 (t) xX rz (t))