Thread: application of Lagranges interpolation

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

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.