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

Multivariable Chain Rule

  • #1
Suppose I have

F(x,y) and y=y(t) and x=x(t)

Therefore,

Ft = Fx*xt + Fy*yt. Right?

Can I write

Ftt = (Fxx*xt + Fyy*yt)*xt + Fx*xtt + (Fxx*xt + Fyy*yt)*yt + Fy*ytt

?

Basically I'm trying to figure out the second derivative by chain rule.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Shouldn't there be some F_xy's and F_yx's in there?
 
  • #3
You're right. I meant to write:


Ftt = (Fxx*xt + Fxy*yt)*xt + Fx*xtt + (Fyx*xt + Fyy*yt)*yt + Fy*ytt
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
You're right. I meant to write:


Ftt = (Fxx*xt + Fxy*yt)*xt + Fx*xtt + (Fyx*xt + Fyy*yt)*yt + Fy*ytt
Looks ok now, good job. Just product rule and chain rule, yes?
 

Related Threads on Multivariable Chain Rule

  • Last Post
Replies
1
Views
835
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
4
Views
291
Replies
10
Views
2K
  • Last Post
Replies
6
Views
3K
Top