Uniform convergence of $f_n(x)=\frac{n^a x^{n-3/2}}{1+x^n}$, $a\in R^+, x \in (0,1)$

Question

I have found the succession $f_n$ pointwise converges to the null function. For the uniform convergence can I calculate $f'_n$ because $Sup_{x\in E}|f_n(x)-f(x)|=Sup_{x\in E}|f_n(x)|$?(E is the uniform convergence set)

Answer 1

It turns out that $f_n'$ is always greater than $0$. On the other hand, $\lim_{x\to1}f_n(x)=\frac{n^a}2$. Since $a>0$, you don't have $\lim_nn^a=0$ and therefore the convergence is not uniform.