Question

Calculus III:

If r(t) = <2t, 3t^2, 3t^3>,
find r'(t), T(1), r''(t), and r'(t) × r ''(t).

Answer 1

Well, we know r'(t) us just the derivative right? I'm sure you can do that :)

Answer 2

As well as r''(t) just the second derivative of r(t)

Answer 3

Take the derivative of each component of the vector separately

Answer 4

The cross product we can just set up as so *only because it's the easiest way I know*
Working with determinants

Answer 5

You there @k8lyn911 ? Is any of this making sense? :)

Answer 6

Sorry. It's been a rough week, and I haven't slept much.
I'm a little overwhelmed right now, so I was hoping to get some notes and build up a study guide for an upcoming test.

Answer 7

since vector addition is component wise, the derivative of a vector is the derivative of each component of a vector

r(t)=<x(t),y(t),z(t)>
r'(t)=<x'(t),y'(t),z'(t)>

Answer 8

r(t) = <2t, 3t^2, 3t^3>
r'(t)=<2,6t,9t^2>
r''(t)=you can do this

Answer 9

https://www.youtube.com/watch?v=qsgK1d-_8ik how to do cross product

Answer 10

this might be an easier way to do the 3x3 determinant

https://www.youtube.com/watch?v=4HpEtkUgdrA

Answer 11

Okay. The answer doesn't really matter anyway; this is just for notes so I can practice later.
I keep getting derivatives and anti-derivatives confused.
Thanks for the help, guys. :)
I can take it from here.