therefore i applied l'hopital s rule to make I hope my differentiation is correct. So do i keep differentiating till I remove the x term from the denominator before i apply the limit?
All too common mistake... you cannot derive via basic powers rule and get . Notice that the result simplifies back to
You need to use the natural log and implicit differentiation to solve for such a derivative.
Take natural log of both sides...
Derive with respect to x on both sides
Substitute for y from original equation