I am not getting the differentiation of 1/2mv? with respect to time?? How does it get converted to dv/dt(v)??

6.6 THE WORK-ENERGY THEOREM FOR A VARIABLE FORCE
We are now familiar with the concepts of work and kinetic energy to prove the work-energy theorem for a variable force. We confine ourselves to one dimension. The time rate of change of kinetic energy is$$\begin{gathered} \frac{dK}{dt}=\frac{d}{dt}\left(\frac{1}{2}m u^2\right) \\ =m\frac{du}{dt}u \\ Fu (\mathrm{from} \mathrm{Newton}\text{'}\mathrm{s} \mathrm{Second} \mathrm{Law}) \\ =F\frac{dx}{dt} \end{gathered}$$