application of Lagranges interpolation

Oct 2012
41
0
uk
Let D:R[x]->R[x]be the differentiation operator D(f(x))=f'(x),prove that
e^tD(f(x))=f(x+t) for a real number t

i dont know how to construct to
proof ,what i wanna to use is lagranges interpolation
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
I really don't know what you are asking. "Lagrange interpolation" has nothing to do with derivatives and "e^tD(f(x))=f(x+t) for a real number t" simply isn't true.