1. The problem statement, all variables and given/known data (From Di Francesco et al, Conformal Field Theory, ex .2) Derive the scale factor Λ of a special conformal transformation. 2. Relevant equations The special conformal transformation can be written as x'μ = (xμ-bμ x^2)/(1-2 b.x + b^2 x^2) and I need to show that the metric transforms as g'μν = Λ(x) gμν 3. The attempt at a solution My attempt was to differentiate the transformation law in order to then use the chain rule (the derivatives are intended as partial): gσλ=dx'μ/dxσ dx'ν/dxλ g'μν For a particular partial derivative I get: dx'μ/dxν = (δμν-2bμxν)/(1-2 b.x + b^2 x^2)- (xμ-bμ x^2)(-2 bν+2b^2 x ν)/(1-2 b.x + b^2 x^2)^2 however plugging this and the other similar term in the chain rule gives rise to a very long expression which does not appear to simplify (I've checked it does in 1D, if all quantities were scalars). Am I doing something wrong, or am I just missing something?