Need help with problem $7$ part$1-6$

Problem $7$

$($Fill in the Blank$)$ : Use the following vector parameterization of a curve to construct a Frenet apparatus in parts $1$ through $6.$

vec$(r)(t)=(3t-t^3)hat(i)+3t^2$hat$(j)+(3t+t^3)hat(k)$

Problem $7-$ Part $1$

$($Fill in the Blank$)$ : Find the first, second, and third derivatives of the vector parameterization.

For full credit, please apply the rules for derivatives and show the relevant calculations.

vec$(r{)}^{\text{'}}(t)=$

vec$(r{)}^{\text{'}\text{'}}(t)=$

vec$(r{)}^{\text{'}\text{'}\text{'}}(t)=$

Problem $7-$ Part $2$

$($Fill in the Blank$)$ : Use the alternative formulation to find the unit tangent vector function.

For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use results from part $1.$

Hint : $t^4+2t^2+1=(t^2+1{)}^2$

hat$(T)(t)=t^4+2t^2+1=(t^2+1{)}^2$hat$(B)(t)=$hat$(N)(t)=(t)=(t)=$