商の微分公式から微分する問題

$${\hspace{10pt}\left\{\frac{f(x)}{g(x)}\right\}' = \frac{f'(x)g(x)-f(x)g'(x)}{\{g(x)\}^2}\hspace{10pt}}$$

$$\begin{aligned} \hspace{10pt}y' & =\frac{(x^2)'(x^4+1) - (x^2)(x^4+1)'}{(x^4+1)^2}\hspace{10pt}\\[1em] & = \frac{2x(x^4+1) - x^2(4x^3)}{(x^4+1)^2}\\[1em] & = \frac{2x^5 + 2x - 4x^5}{(x^4+1)^2}\\[1em] & = \frac{-2x^5 + 2x}{(x^4+1)^2}\\[1em] & = \frac{-2x(x^4 -1)}{(x^4+1)^2}\\[1em] \end{aligned}$$