Tangent Vector for Vector Function?

[fball558]

Tangent function vector?

Homework Statement

i know the formula for this problem. My homework was to like 5 of these and got the other 4. now stuck on the algebra part. please take a look and let me know where to go from here.
problem is
consider the vector function given below:
r(t) = <8sqrt(2)t, e^(-8t), e^(8t)> only the 2 in the x cordinate is square root
find the unit tangen vector

it will be r'(t) / |r'(t)|

derivative of r(t) = 8sqrt(2) , -8e^(-8t) , 8e^(8t)

then i get stuck on the magnitude of this. i know it is each component squared then square root of all them added togeather.
i get

128 + 64e^(-64t) + 64e^(64t)
then square root this whole thing.

im not sure how to simplify the whole e thing.
any help would be great!
thanks

 

[Mark44]

I didn't see it at first, but |r'(t)| is incorrect. When you square e^8t you don't get e^64t; you get e^16t.

Also, you might want to keep in mind that (e^8t + e^-8t)² = e^16t + 2 + e^-16t

 

[fball558]

ok thanks i got it now!