高微習題証明題請幫忙

let f be a continuous function on [0.無限) that satisfies |f(x)| <= a(1+x)^N e^bx for some a,b N>=0.The Laplace transform of f is the function L[f] defined on (b,無限) by

L[f](s)=(積分0到無限) e^-sx f(x)dx

suppose that f is of class c1 on [0,無限) and that f ' satisfies the same sort of
exponential growth condition as f. show that L[f '](s)=sL[f](s)-f(0)