Second derivative in terms of x and y?

  • #1

Homework Statement



Find y" in terms of x and y:

y^2 + 2y = 2x + 1

Homework Equations



N/A

The Attempt at a Solution



I found the first derivative:

y^2 + 2y = 2x + 1
2yy'+2y'=2
2y'.(y+1)=2
y'=2/2(y+1)
y'=1/(y+1)

But I'm having trouble moving on from there.
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,368
1,035

Homework Statement



Find y" in terms of x and y:

y^2 + 2y = 2x + 1

Homework Equations



N/A

The Attempt at a Solution



I found the first derivative:

y^2 + 2y = 2x + 1
2yy'+2y'=2
2y'.(y+1)=2
y'=2/2(y+1)
y'=1/(y+1)

But I'm having trouble moving on from there.
Now, take the derivative of y'.

Sure it will have y' in it, but then substitute the result you have for y' into that.
 
  • #3
Now, take the derivative of y'.

Sure it will have y' in it, but then substitute the result you have for y' into that.

alrighty so...

y" = derivative of 1/y+1

= (1)(y+1)^-1 ... then use product rule

= 0 + (-1(y+1)^-2)y' ... then plug in y'

= - [1/(y+1)]/(y+1)^2 ... combine

y" = - 1/(y+1)^3 final answer


......

I think I did it right. Does this satisfy "in terms of x and y?"
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,368
1,035
Looks good !
 
  • #5
thanks!
 

Related Threads on Second derivative in terms of x and y?

Replies
4
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
10
Views
10K
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
1
Views
10K
  • Last Post
Replies
3
Views
22K
Top