$c(t) = (x(t),y(t),z(x,y)) = (7t + 6, 9t^2 + 6t, (7t + 6)^2 + \sin [(7t + 6)(9t^2 + 6t)])$?
just differentiate the components, your vector is $\left< x'(t), y'(t), z'(t) \right>$