Derivative of the norm of a Quaternion in Mathematica

Question

I am rather new to Mathematica and am using it to work on Quaternions at the moment. In one particular case I would like to obtain a derivative involving the norm of a Quaternion, like the following:

In[1]:= << Quaternions`

D[Norm[Quaternion[a, b, c, d]], b]
                                                (0,1,0,0)
Out[6]= Norm'[Quaternion[a, b, c, d]] Quaternion         [a, b, c, d]

Mathematica is actually capable of computing the Norm of a Quaternion but does someone know whether it can expand the Norm function so that the above input yields the expanded derivative (//FunctionExpand did not change anything on the output...).

Any hints are appreciated, thanks!

Answer 1

The Norm of a quaternion is simply Sqrt[a^2 + b^2 + c^2 + d^2]. So, any one of the partial derivatives can be determined by: http://www.wolframalpha.com/input/?i=derivative+of+Sqrt%5Ba%5E2+%2B+b%5E2+%2B+c%5E2+%2B+d%5E2%5D