Expert: Paul Klarreich - 10/30/2005

Question
Hello, i'm doing an online calculus course and am stuck on a problem relating to derivatives. Can you explain it for me? I know derivatives aren't listed in your expertise, but i'm hoping you can help me.

here's the problem:
find dy/dx|x=1
y=(2x^7 - x^2)[(x-1)/(x+1)]

thanks for any help you can offer!
-Stephen K.

Answer
Hi, Stephen,

If y = (2x^7 - x^2)[(x-1)/(x+1)]  then this is nothing more than a fairly messy quotient rule problem.  (Also the product rule, but we can get around that.)

Best is to write the problem as:
   (2x^7 - x^2)(x - 1)
y = -------------------
          x + 1

Next multiply out on top:
   2x^8 - x^3 - 2x^7 + x^2  (Top)
y = ------------------------
           x + 1

and then use the quotient rule:

dy   (16x^7 - 3x^2 - 14x^6 + 2x)(x + 1) - (Top)(1)
-- = -----------------------------------------------
dx                    (x + 1)^2


You could do some simplifying (shouldn't take more than 20 minutes) but at this point you can substitute  x = 1.  The values should come out to something like:

dy   (16 - 3 - 14 + 2)(2) - (0)(1)   1
-- = ----------------------------- = --
dx               4                   4

BY THE WAY, although I don't mind answering any question you have, there is one point I should make:

I shall be on vacation for some days coming up. If you are paying money for this online course, they should be using some of your hard-earned money to pay someone to answer your questions.  Otherwise they are just trying to put some faculty out of work.