Finding speed/magnitude of r prime

Question

I need to find the speed of a particle with $r(t) = \langle \sqrt{2}t i, e^t j, e^{-t} k \rangle$

I have $r' = \langle\sqrt{2}i, e^tj, -e^{-t}k\rangle$

and got $\|r'(t)\|= \sqrt{ 2 + e^{2t}+e^{-2t}}$

But the answer is listed as just $\|r'(t)\| = e^t+e^{-t}$

How are they getting this?

Answer 1

Note that $2+e^{2t}+e^{-2t}=(e^t)^2+2e^te^{-t}+(e^{-t})^2=(e^t+e^{-t})^2$