First find the derivative at the given point and later divide by the magnitude of this derivative.
Derivative: r' (t) = 2t i+ 2j t
Magnitude:
[tex] \sqrt{ (2t)^{2} + (2t)^{2} } = \sqrt{8t^2} =2 \sqrt{2} t[/tex]
Now use the value t =1
Derivative: 2(1)i + 2(1)j = 2i + 2j
Magnitude: 2√2
Unit vector: [2i + 2j] /[2√2] = (√2)/2 i + (√2)/2 j
