I'm stuck on a question from my chapter review homework. It appears the textbook has used the Chain Rule, but we were never taught how to use the Chain Rule in this context, so I don't know how to apply it.
How would I work this question out?
Find the derivative.
I tried to chain the top and then the bottom separately- obviously that can't be right.
This is what I tried to do:
I tried to chain the top to find the derivative of f(x), which is the top function.
I tried to chain the bottom to find the derivative of g(x), which is the bottom function.
I got this, and I tried to use the quotient rule after I used the chain rule.
But the book chained the whole function. They threw the whole original function out front, as you would do with the chain rule. This is their response:
If logarithmic differentiation is needed to do that question, we skipped that topic in this unit, and as far as I know, we're not responsible for it.
If this is a logarithmic differentiation type question that was on the review, I guess I shouldn't have attempted it yet. This always happens to me! I try a question, get frustrated because I can't do it, and then later learn it wasn't something we were taught yet! LOL
your derivative for the second is not correct, you should have 6x^2 not 6x. maybe that's why you have been having problems.
logarithmic differentiation is not REQUIRED, it is just another way to do the problem. this problem can be done with only the chain, quotient and product rules.
yes, keep going.
TheEmptySet has a good point. it would seem that the book did use logarithmic differentiation. it can be done without it though, so continue. i also agree with TheEmptySet in that, if you can learn logarithmic differentiation by yourself, you should. you are familiar with the laws of logarithms right?