derivative of vector r(t)=<e^t cos(t), e^t sin(t), t>

[acpodgorski]

i am given the vector r(t):

r(t) = < e^t cos(t), e^t sin(t), t >

i want to find its derivative and then the magnitude of its derivative. This is all in order to find the curvature at (1, 0, 0).

I thought that the derivative woudl then be:

<-(e^t)(sin(t)) + (e^t)(cos(t), (e^t)(cos(t) + (e^t)(sin(t), 1>

and then i found hte magnitude to be:

(1 + (2e^2t) + 1)^1/2

Is this right so far? I am a little rusty on my derivatives. Thank you!

 

[pka]

It appears correct to me. But I have not actually done the operations.
Your ideas are correct.