I've attached the problem statement. I was thinking of defining the derivative, L(h) as some differential df_{t}*[f_{1}(t) f_{2}(t) ... f_{m}(t)] with df_{t}(h)=f'(t)*h. I just need to check that it satisfies the definition of lim h->^{f(t+h)-f(t)-L}^{(h)}/h but I'm getting stuck. Is the the right approach? Any suggestions?