\[ \vec {f}'(t)=\vector {\answer {2t},\answer {0},\answer {1}}, \]
\[ \utan (t)=\vector {\answer {\frac {2t}{\sqrt {1+4t^2}}},\answer {0},\answer {\frac {1}{\sqrt {1+4t^2}}}} \]
Find the derivative \(\vec {f}'\) and the unit tangent vector \(\utan \) for \(\vec {f}(t)=\vector {t^2,1,t}\).