Estimates concerning difference quotients of Sobolev function

Question

for a Sobolev function $f\in W^{1,p}(\mathbb{R}^n)$ for some $p>1$, let's consider the difference quotient $\Delta_{\tau,i} f(x) = \frac{f(x+h e_i)-f(x)}{\tau}$ for some $\tau>0$ and any $i=1,2,...,n$. I know that there are certain estimates concerning the $L^p$-norm of $Du$ and the difference quotient but I am looking at some a.e. pointwise estimate of the form $$|\Delta_{\tau,i} f(x)|\leq C |D_i u(x)|$$ or $$|D_i u(x)|\leq C|\Delta_{\tau,i} f(x)|$$ with $C$ a constant that probably depends at least on $h$. Are there any known results like this? I could not find anything until now so probably any of the above estimates does not hold...Thanks in adcance for any help!