The first appearance in print of l'Hospital's rule was in the book Analyse des Infiniment Petits published by the Marquis de l'Hospital in 1696. This was the first calculus textbook ever published and the example that the Marquis used in that book to illustrate his rule was to find the limit of the function

$y=\dfrac{\sqrt{2 a^3 x - x^4}-a\sqrt[3]{a a x}}{a-\sqrt[4]{a x^3}}$

as $x$ approaches $a$, where $a > 0$. (At that time it was common to write $aa$ instead of $a^2$.) Solve this problem, your answer may depend upon $a$.