derivatives of Kinetic Energy I read that derivative of Kinetic Energy function = $F.v$ while I got $mv$ when I differentiated it with respect to velocity. 
The way I did it is: 
$\frac{dK}{dv} = \frac{1}{2} m . \frac{d}{dv} v^2$ 
So I assumed that the mass is fixed and I differentiated the squared velocity by taking the (2) down and subtracting (1) from the exponent, which gave me $2v$ for $\frac{d}{dv} v^2$
Would you clarify the correct derivative of Kinetic Energy as well as the $F$ variable? And what does the derivative in this case represent?

$$\frac{d v^2}{dt}=2v\frac{dv}{dt}$$
$$\implies \frac{dK}{dt}=\frac{1}{2}m\frac{d v^2}{dt}=mv\frac{dv}{dt}$$
but $$m\frac{dv}{dt}=F$$
thus
$$\frac{dK}{dt}=Fv$$
which represents the power of force $F$ ,( in Watt).
