- #1

Nero26

- 21

- 1

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.

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.

Last edited: