uniform convergent Given f is a differentiable function. Define $$f_n(x)=n\left(f\left(x+\frac{1}{n}\right)-f(x)\right)$$, prove that $f_n$ is uniformly converge to $f'$
I have tried to make these equations:
$n(f(x+\frac{1}{n})-f(x))=\frac{f(x+\frac{1}{n})-f(x)}{1/n}$ and taking limits as n $\to\infty$ but i got stuck to prove its uniform convergent

rather than have $n\to\infty$ we can say $\delta x\to0^+$ from $\delta x=\frac{1}{n}$ and then we get:
$$\lim_{\delta x\to 0^+}\frac{f(x+\delta x)-f(x)}{\delta x}=f'(x)$$
this is of course dependent on that fact that $f$ is a continuous function for the range we are looking at and is differentiable on this set. Now you need to consider if this function is continuous.
