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Homework Help: Composition of two differentiable functions

  1. Apr 3, 2010 #1

    michonamona

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    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
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  3. Apr 3, 2010 #2

    Hurkyl

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

    Fredrik

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    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

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    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
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