I want to construct a frenet curve $Y: \Bbb R \to \Bbb R^3$ with constant curvature $K$ and torsion $T$. I figured I'd start with calculating the derivatives of $K$ and $T$ but I don't know how to differentiate those expressions. They are specifically,
$$K = \|(Y' \times Y'')\|/\|Y'\|^3,$$
$$T = \det[Y', Y'', Y''']/\|Y' \times Y''\|^2.$$
Thanks for your time!