Let r(t)=〈t2,1−t,4t〉. Calculate the derivative of r(t)⋅a(t) at t=2 Assuming that a(2)=〈7,−3,7〉 and a′(2)=〈3,2,4〉

ddtr(t)⋅a(t)|t=2=

101

Step-by-step explanation:

We are given that

r(t)=

We have to find the derivative of r(t).a(t) at t=2

a(2)=<7,-3,7> and a'(2)=<3,2,4>

We know that

Using the formula

Substitute t=2

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8