F\: = m_{0}\cdot\frac{\mathrm{d} }{\mathrm{d} t}\left ( \frac{1}{\sqrt{\frac{1}{v^{2}}-\frac{1}{c^{2}}}} \right ) = m_{0}\cdot\left ( -\frac{1}{2} \right )\cdot \left ( \frac{1}{v^{2}}-\frac{1}{c^{2}} \right )^{-3/2}\cdot \left ( -2v^{-3} \right )\cdot \frac{\mathrm{dv} }{\mathrm{d} t} = m_{0}\cdot \left ( 1-\frac{v^{2}}{c^{2}} \right )^{-3/2}\cdot \frac{\mathrm{dv} }{\mathrm{d} t}