Question

Let r(t)=〈t2,1−t,4t〉. Calculate the derivative of r(t)⋅a(t) at t=2

Answer 1

Answer:

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

$\frac{d(uv)}{dx}=u'v+v'u$

Using the formula

$\frac{d(r(t)\cdot at(t))}{dt}=r'(t)\cdot a(t)+r(t)\cdot a'(t)$

$\frac{d(r(t)\cdot at(t))}{dt}=\cdot a(t)+\cdot a'(t)$

Substitute t=2

$\frac{d(r(t)\cdot at(t))}{dt}_|t=2=\cdot a(2)+\cdot a'(2)$

$\frac{d(r(t)\cdot at(t))}{dt}_|t=2=\cdot +\cdot$

$\frac{d(r(t)\cdot at(t))}{dt}_|t=2=28+3+28+12-2+32=101$