How can the chain rule be used to simplify the energy transformation equation?

[coverband]

How does $$\frac{d\dot{x}}{dx}\frac{dx}{dt} =\frac{d}{dx}(\frac{1}{2}{\dot{x}}^2)$$

Thanks

 

[marcusl]

Apply the chain rule, that is (I'll change variables so as not to do the problem for you exactly):

$$\frac{d}{dv}u^2=2u\frac{du}{dv}$$