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I Elementary question on composition of functions

  1. May 17, 2018 at 9:43 AM #1
    Helo, given ##f:R^n\rightarrow R^m## and ##g:R^m\rightarrow R^e## both class ##C^m##. Is the composition ##g\circ f## of class ##C^m## ?.
     
  2. jcsd
  3. May 17, 2018 at 10:33 AM #2

    MathematicalPhysicist

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    Yes, use the chain rule to prove it.
     
  4. May 18, 2018 at 3:59 AM #3

    MathematicalPhysicist

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    BTW, I believe this exercise appears in Munkres Analysis on Manifolds with a suitable guidance, but I am not 100% sure.
     
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