Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Composition of two differentiable functions

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Is the composition of two differentiable functions always differentiable?

    E.x.

    h(x) = sin(x)
    k(x) = 1/x for x not equal 0

    Does this automatically mean h(k(x)) is differentiable?

    Thank you,

    M
     
  2. jcsd
  3. Apr 3, 2010 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sure. You even know a formula for the derivative, right?
     
  4. Apr 3, 2010 #3

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I'll just comment about one of my little pet peeves. h(k(x)) is a number, not a function. The function you have in mind is written as [itex]h\circ k[/itex] or [itex]x\mapsto h(k(x))[/itex]. (Note the special "mapsto" arrow).
     
  5. Apr 4, 2010 #4
    Thank you for your replies.

    So the composition of two differentiable functions is ALWAYS differentiable? I know the derivative of their composition, we just use the chain rule.

    Thanks Fredrik. I never thought about that. Now I understand why they always use LaTeX Code: h\\circ k when referring to composition of functions.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook