Given that V = xyz(r^−7), find the first partial derivative of V (wrt x) and deduce that the second partial derivative of V (wrt to x) is
−21xyz(r^−9) + (63x^3)yz(r^−11)
NB: d = delta sign, del = del function (upside down triangle)
I've tried it several times now. I can see where the coefficents will eventually come from being multiples of 7, but I can't get the answer above. Can anyone help? Thanks.
Thanks! The next part of the Q is:
Use symmetry to write down the corresponding expressions for the second derivatives of V wrt to y and z.
Deduce that (del)^2(V) = 0.
The second derivative of V wrt y would be the same but using dr/dx = y/r etc. yeah? Once I have derivatives wrt y and z, would their sum equal 0?