Differentiation of a polynomial function

  • Thread starter Duane
  • Start date
  • #1
8
0

Main Question or Discussion Point

Hi guys

I'm getting into a little trouble when differentiating polynomial functions.

How do you differentiate

f(x)=ax+b/cx+d ?

Is there other ways of calculating this apart from the chain rule ?


Thanks for any help.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,806
932
Surely by the time you are taking Calculus you should know that what you give is NOT a polynomial!! And I can't imagine why you would think about the chain rule. That is a quotient so use the quotient rule.
 
  • #3
8
0


Sorry I messed up.
What I meant was a "rational" function.

Are "rational" and "quotient" synonymous ?

By applying the quotient rule, I get

(ax+b/cx+d)'= [(cx+d)(ax+b)'-(ax+b)(cx+d)'] / (cx+d)^2

= [a(cx+d)-c(ax+b)] / (cx+d)^2

how to proceed ?
 
  • #4
Stephen Tashi
Science Advisor
7,016
1,237
You can multiply the terms in the top of the fraction [itex] \frac{a(cx+d) - c(ax+b)}{(cx+d)^2}[/itex] and then combine like terms. I don't see anything that "simplifies" beyond that.

A point about notation, you should write the original function as (ax+b)/(cx+d) to mean [itex] \frac{ax+b}{cx+d} [/itex] instead of writing it as (ax +b/cx + d}, which means [itex] ax + \frac{b}{c} x + d [/itex].

Better yet, look at the sticky thread:
Physics Forums > PF Lounge > Forum Feedback & Announcements
LaTeX Guide: Include mathematical symbols and equations in a post
 

Related Threads on Differentiation of a polynomial function

  • Last Post
Replies
4
Views
2K
Replies
1
Views
4K
Replies
3
Views
682
Replies
2
Views
938
Replies
1
Views
5K
Replies
4
Views
1K
Top