先纠正一下：E=mc^2=Ek+m0c^2=m0c^2/sqrt(1-v^2/c^2)
然后推导,但要用到微积分：
dE/dt=Fv=vd(mv)/dt=mvdv/dt+v^2dm/dt
dE=mvdv+v^2dm
=m0vdv/sqrt(1-v^2/c^2)+m0v^2d[1/sqrt(1-v^2/c^2)]
=-m0c^2d[sqrt(1-v^2/c^2)]+m0v^3*(1-v^2/c^2)^(-3/2)dv/c^2
=-m0c^2d[sqrt(1-v^2/c^2)]+m0c^2(v^2/c^2)*(1-v^2/c^2)^(-3/2)d(v^2/c^2)/2
=m0c^2d[1/sqrt(1-v^2/c^2)]
积分得：
E-Eo=m0c^2[1/sqrt(1-v^2/c^2)-1]=mc^2-m0c^2
比较可得：
E=mc^2
Eo=m0c^2