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

Composition Of Functions

  • Thread starter Lancelot59
  • Start date
  • #1
634
1
I have two functions:

[tex]f(x,y,z)=\sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\vec{c}(t)=<cos(t),sin(t),1>[/tex]

I need to find:
[tex](f \circ c)'(t)[/tex]
and
[tex](f \circ c)'(0)[/tex]

I don't have any answers to work with, but I'm guessing I just stick f into c to get this:

[tex]\vec{c}(t)=<cos(\sqrt{x^{2}+y^{2}+z^{2}}),sin(\sqrt{x^{2}+y^{2}+z^{2}}),1>[/tex]

Then once I have that get the derivative matrix and plug in 0?
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
what you didn't doesn't make sense

c maps the scalar t to the vector (x(t),y(t),z(t))
f maps the vector (x,y,z) to a scalar f(x,y,z)

so you want to find f(c(t))
f(c(t)) will map t to a scalar
 
  • #3
634
1
what you didn't doesn't make sense

c maps the scalar t to the vector (x(t),y(t),z(t))
f maps the vector (x,y,z) to a scalar f(x,y,z)

so you want to find f(c(t))
f(c(t)) will map t to a scalar
I follow you. So I really should be working with this after I put everything together?

[tex]f(x,y,z)=\sqrt{(cos(t))^{2}+(sin(t))^{2}+(1)^{2}}[/tex]
 
  • #4
lanedance
Homework Helper
3,304
2
looks better, and if you want to include everything explicitly
[tex](f \circ c)(t) = f(c(t)) = f(x(t),y(t),z(T))=\sqrt{(cos(t))^{2}+(sin(t))^{2}+(1)^{2}}[/tex]
 
  • #5
Char. Limit
Gold Member
1,204
13
I follow you. So I really should be working with this after I put everything together?

[tex]f(x,y,z)=\sqrt{(cos(t))^{2}+(sin(t))^{2}+(1)^{2}}[/tex]
Yep. Now just simplify that expression.
 
  • #6
634
1
...I did all that just to get the square root of 2? What a rip off. So the function is just gonna be equal to the root of two, and the derivative is zero?
 
  • #7
Char. Limit
Gold Member
1,204
13
...I did all that just to get the square root of 2? What a rip off. So the derivative of the function at any point is therefore a constant root 2?
no, the function at any point is a constant root 2.
 
  • #8
HallsofIvy
Science Advisor
Homework Helper
41,794
925
[itex]f\circ c(x)[/itex] means f(c(x)) not g(f(x)).
 

Related Threads for: Composition Of Functions

  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
4
Views
823
  • Last Post
Replies
4
Views
1K
Replies
4
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
5K
Top