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?

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- Apr 16th 2008, 03:59 AMasheslimits(l'hopital's rule)
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?

- Apr 16th 2008, 04:24 AMmr fantastic
- Apr 16th 2008, 06:04 AMcolby2152
Mr. Fantastic's answer is correct, but I have one point to make...

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.

Start with:

Take natural log of both sides...

Derive with respect to x on both sides

Substitute for y from original equation

- Apr 16th 2008, 06:42 AMIsomorphism
Interestingly we were taught to do this with a different perspective.

Now substitute y=x