• Support PF! Buy your school textbooks, materials and every day products Here!

Forgot my chain rule T.T

  • Thread starter l46kok
  • Start date
  • #1
296
0

Homework Statement


y = 2x / (1+x^2)^2

Find dy/dx

Homework Equations


Chain rule


The Attempt at a Solution


I completely forgot how to apply the chain rule.. I mean, I can always apply the quotient rule, but I'm sure this is 1000 times easier if you can apply the chain rule. Do you do something like

u = 1+x^2
du = 2x

so

y = du/u

But I may be getting confused with substitution rule with integration.. it's been a while since I touched calculus.. any suggestions?
 

Answers and Replies

  • #2
590
0
Chain rule goes something like
dy/dx=dy/du*du/dv*......*df/dx .

It is usually used when you when you have a nested combination of functions, ie functions within functions.

For your question, you need to use both the quotient rule as well as the chain rule ( (1+x^2)^2, which is the funtion 1+x^2 within a squaring function ) .

Can you finish your problem now ?
 
  • #3
296
0
Chain rule goes something like
dy/dx=dy/du*du/dv*......*df/dx .

It is usually used when you when you have a nested combination of functions, ie functions within functions.

For your question, you need to use both the quotient rule as well as the chain rule ( (1+x^2)^2, which is the funtion 1+x^2 within a squaring function ) .

Can you finish your problem now ?
Right.. that's the BRUTE force way to do it.

I was wondering if there was a way to finish this without even applying the quotient rule
 
  • #4
402
0
if you dont want to use the quotient rule you can bring the denominator up top so:[tex] y= 2x (1+x^2)^{-2}[/tex] now use the product rule
 
  • #5
cristo
Staff Emeritus
Science Advisor
8,107
73
Right.. that's the BRUTE force way to do it.

I was wondering if there was a way to finish this without even applying the quotient rule
Yes, just write the expression as 2x(1+x2)-2, and use the product rule on this.
 
  • #6
296
0
if you dont want to use the quotient rule you can bring the denominator up top so:[tex] y= 2x (1+x^2)^{-2}[/tex] now use the product rule
I guess that's true, but when I saw the relating terms, I was thinking this could be solved by ONLY using chain rule.

I guess it's impossible.
 

Related Threads on Forgot my chain rule T.T

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
977
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
845
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
745
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
8
Views
735
  • Last Post
Replies
5
Views
829
Top