These are given by:
$$\frac{dx}{dt} = \frac{d}{dt}(1+2\sqrt{t}), \quad \frac{dy}{dt} = \frac{d}{dt}(t^{3}-t), \quad \frac{dz}{dt} = \frac{d}{dt}(t^{3}+t)$$
which simplifies to:
$$\frac{dx}{dt} = \sqrt{2}, \quad \frac{dy}{dt} = 3t^{2}-1, \quad \frac{dz}{dt} =
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