Hi, I was wondering if anyone knows how to differentiate
m(dv/dt)=mg-kv^2
I know partial fractions must be involved however I can't get beyond this point.
thank-you.
If you expect to have to use partial fractions, you're probably asking how to solve this differential equation (though integration, NOT differentiation).
$\displaystyle \displaystyle \begin{align*} m\,\frac{dv}{dt} &= mg - kv^2 \\ \frac{dv}{dt} &= \frac{mg - kv^2}{m} \\ \frac{dt}{dv} &= \frac{m}{mg - kv^2} \\ t &= \int{\frac{m}{mg - kv^2}\,dv} \\ t &= \int{\frac{m}{\left(\sqrt{mg} - \sqrt{k}\,v\right)\left(\sqrt{mg} + \sqrt{k}\,v\right)}\,dv} \end{align*}$
and you can now apply Partial Fractions
Well then you should show what you have tried. A differential equation is an equation that involves derivatives, so the solution of a differential equation is to find the family of functions that will satisfy the differential equation. In this case, you are trying to find a function $\displaystyle \displaystyle v(t)$.