Let [tex]\mathbf p(t)=(x(t),y(t),z(t))[/tex] denote the particle's position. Then its velocity is given by
[tex]\mathbf v(t)=\dfrac{\mathrm d\mathbf p}{\mathrm dt}=(x'(t),y'(t),z'(t))[/tex]
[tex]\mathbf v(t)=(18t^2-18t,0,4t-4)[/tex]
The speed is then given by the absolute value/magnitude/norm of the velocity function,
[tex]\|\mathbf v(t)\|=\sqrt{(18t^2-18t)^2+(4t-4)^2}[/tex]
