m^2+m^2+m^2+.........up to m term =m^2*m=m^3 Which is identity .So we use derivative for this identity. Now, d/dm(m^2+m^2+m^2+.....up to m term)=d/dm(m^3) Or 2m+2m+2m+........up to m term=3m^2 Or 2m*m=3m^2 Or 2m^2=3m^2 but it is not possible.So there should be some mistakes.But I'm not getting it. What I suspect are as follows: In L.H.S we differentiated first,then add all terms.In R.S we added all then differentiated it.Is the mistake for maintaining different orders of operation? I suspect another reason like while differentiating R.S, number of terms is considered as variable and multiplied with m^2 that leads to m^3,but as it is no. of terms if I assume it as constant then, m*d/dm(m^2)=m*2m=2m^2,which matches with L.S. Is this okay?or something else? Thanks for your help.