Problem $15.$ Find $y^{\text{'}}$ if $x^y=y^x$ and then evaluate $y^{\text{'}}(1)$ if $y(1)=1.$

$1$

Question $1$: A certain Professor Amongus claims that the order in which a fixed set of elements is inserted into an AVL tree does not matter$-$the same tree results every time. Give a small example that proves Professor Amongus wrong. $(20$ points$)$

Question $1$: A certain Professor Amongus claims that the order in which a fixed set of elements is inserted into an AVL tree does not matter$-$the same tree results every time. Give a small example that proves Professor Amongus wrong. $(20$ points$)$