Originally Posted by
TheEmptySet You need to show that the units match on both sides of the equation.
Force has units
$\displaystyle F=\frac{(\text{kg})(\text{m})}{\text{s}^2}$
$\displaystyle m=\text{kg}$
$\displaystyle v=\frac{\text{m}}{\text{s}}$
Now we need to take the derivative on the right hand side
$\displaystyle \frac{d}{dt}(mv)=\left( v\frac{dm}{dt}+m\frac{dv}{dt}\right)$
So now analyze the units
$\displaystyle \frac{\text{m}}{\text{s}}\cdot \frac{\text{kg}}{\text{s}}+\text{kg}\cdot \frac{\text{m}}{\text{s}^2}$
So the units on both sides are the same