Find the derivative......

[hhlebiczki]

Hello!
I have been trying to find the first derivative of the following function for about a week and I'm going bonkers.
I have NO IDEA how to deal with the numerator. Normally, it wouldn't be a problem, but I have NO IDEA how to deal with the negative exponent. HELP!!!!!


THANKS in advance!!!!!


m(r) = 15000r / (1- (1+ r /12)^-360)

 

[renegade05]

First is this your problem:

\(\displaystyle m(r)=\frac{15000r}{1-(1+\frac{r}{12})^{-360}}\)

Ya this one could be messy to do by hand, nevertheless we will need to use a quotient rule. Have you learned about the quotient rule.

Go here if not:
http://en.wikipedia.org/wiki/Quotient_rule

Your problem will essentially be:

\(\displaystyle m'(r)=\frac{[\frac{d}{dr}(15000r)*(1-(1+\frac{r}{12})^{-360})]-[(15000r)*\frac{d}{dr}(1-(1+\frac{r}{12})^{-360})]}{(1-(1+\frac{r}{12})^{-360})^2}\)

 

[hhlebiczki]

Exactly! I can get to that point but that's where I get stumped!
All I need to be able to do is to simplify the d/dx of the original denominator and I'd be set.

Can anyone PLEASE PLEASE PLEASE help me with that?!?! Seriously, this problem kept me up last night!

There is a problem in my book that uses the same formula, but it's the example where they show how to use the calculator to solve! But I have to turn it with all work show by hand.

Just my luck..........................;-).

 

[Deleted member 4993]

Exactly! I can get to that point but that's where I get stumped!
All I need to be able to do is to simplify the d/dx of the original denominator and I'd be set.

Can anyone PLEASE PLEASE PLEASE help me with that?!?! Seriously, this problem kept me up last night!

There is a problem in my book that uses the same formula, but it's the example where they show how to use the calculator to solve! But I have to turn it with all work show by hand.

Just my luck..........................;-).

Are you saying - we should do the "algebra" for you and you'll copy it down?

Does not work that way! We need to see how far you did go - and we can check your work.

But slogging through that algebra is not my cup of coffee .....

 

[renegade05]

hhlebiczki:

Firstly, it's d/dr not d/dx in this situation - you should pay attention to subtleties like these.

Second, what d/dr in the denominator? Where EXACTLY are you stuck. I'm with subhotosh I don't want to do all that algebra. If you are just stuck on one part though, then we can help you get started with that part. Be specific and let us know what you have tried and why you are stuck.