# real analysis – Uniform convergence of a sequence of functions to a function (g) but their derivatives converge pointwise to a function which is not (g’)

Question is that find a sequence ($$f_n$$) of continuously differentiable real functions defined on $$(0,1)$$ converges uniformly to a differentiable function ($$g$$) and ($$f_n’$$) converge pointwise to a function that is not ($$g’$$). I am trying to find this function. I think that $$frac{x}{1+x^2n^2}$$ converges uniformly to zero on (0,1) and derivate $$frac{1-n^2x^2}{(1+x^2n^2)^2}$$ converges pointwise to 1 at zero and 0 for all other points. Is my logic correct? Any help will be appreciated.Thanks