I'm asked to show that d(ˆAˆB)dλ = dˆAdλˆB+ˆAdˆbdλ
With λ a continuous parameter. Should I use the definition dˆAdλ = limϵ→0ˆA(λ+ϵ)−ˆA(λ)ϵapplied to ˆAˆB like d(ˆAˆB)dλ = limϵ→0ˆA(λ+ϵ)ˆB(λ+ϵ)−ˆA(λ)ˆB(λ)ϵand do some algebra to get the RHS of the first equation, or I'm missing something?Another interesting derivative to pay attention to is: ddλexp(ˆA(λ)) ?
Answer
A(λ+ϵ)B(λ+ϵ)=(A(λ)+ϵ˙A)(B(λ)+ϵ˙B)=A(λ)B(λ)+ϵ(˙AB+A˙B)+o(ϵ2)
No comments:
Post a Comment