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Proof that a function composition is differentiable

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Let f:R->R, differentiable, f(1)=1 and f'(1)=2.


    2. Relevant equations
    Prove that g:R->R such that g(x)=f(x)Arctg(f(x)) is differentiable in x=1 and calculate g'(1)


    3. The attempt at a solution
    I would prove it saying that if a function is differentiable then the product and composition it's differentiable, but I don't think is that simple, am I wrong?

    Thanks!
     
  2. jcsd
  3. Apr 11, 2012 #2

    SammyS

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    It does appear to be that simple, so I suppose that means, that you are wrong about it not being that simple.

    Now, calculate g'(1) .
     
  4. Apr 11, 2012 #3
    Thanks! ;)
     
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