Eulerian vs. Lagrangian description

Homework Statement

A particle moves so that $$\vec{x} \equiv [x_0 exp(2t^2), y_0 exp(-t^2), z_0 exp(-t^2)]$$. Find the velocity of the particle in terms of $$x_0$$ and t (the LAgrangian description) and show it can be written as $$\vec{u} \equiv (4xt, -2yt, -2zt),$$ the Eulerian description

The Attempt at a Solution

$$\vec {u} = [4tx_0 exp(2t^2), -2ty_0 exp(-t^2), -2tz_0 exp(-t^2)]$$

The exp's go to 1 !!?

Thanks

No, i suppose it's just that in your velocity vecotr you can substitute the term $$x_0exp(2t^2)$$ with x - "first part" from your $$\vec{x}$$ vector and so on
Let's consider a single function $$f(x)=exp(2x)$$. Obviously, $$\frac{df}{dx}=2exp(2x)$$. And you can write $$\frac{df}{dx}=2f(x)$$, which is true for all x, but doesn't really mean anything.
E:and so, in your example, you just get $$x_x=x_0exp(2t^2)$$, $$u_x=4tx_0exp(2t^2)=4tx$$