1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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

    michonamona

    User Avatar

    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
     
    michonamona, Apr 3, 2010
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Apr 3, 2010 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    michonamona

    User Avatar

    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.
     
    michonamona, Apr 4, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook