Q. Consider the sequence of real-valued functions $\{f_n\}$ defined by $$f_n(x)=\frac {1}{1+nx^2}.$$ Assuming the fact that $\{f_n\}$ converges uniformly to a function $f$ find out real numbers $x$ for which $$f'(x)=\lim\limits_{n \to \infty} f'_n(x).$$
Here each $f_n$ is a continuous function. If the sequence $f_n$ were to converge uniformly to a function $f$, then $f$ must have been continuous too. But $$f(x) = \begin{cases} 0, & \text{if $x \neq 0$} \\ 1, & \text{if $x=0$} \end{cases}$$ is discontinuous.
Am I making mistakes here? I am not able to comprehend this question.