Chain rule for one variable

Question

I have a simple question.

Can the equation (1) be proven using equation (2)

(1) $\nabla_x U(x)\dot x=\frac{d}{dt} U(x) $

(2)$\frac{\partial U(x)}{\partial x} \frac{dx}{dt} = \frac{dU(x)}{dt} $ ?

Or have I misinterpreted the chain rule ?