Is Susskind's claim that d/dt (y')^2 = 2y'' correct?

[lolgarithms]

for example, isn't the derivative of the first derivative squared:

d/dt (y')^2 = 2y'y''? why does susskind claim it is 2y'', in his classical lecture 3?

 

[Hepth]

Ahh, he's doing lagrangian mechanics.
He is NOT doing
$$\frac{d}{dt} y'^2$$

He is using euler's equations and doing instead:
$$\frac{d}{dt} \frac{\partial}{\partial y'} (y'^2) = \frac{d}{dt} 2 y' = 2 y''$$
The two dissappears from the kinetic energy term because its (1/2) m v^2.