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Find the derivative of inverse of this function

  1. May 27, 2013 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    Let f be a real valued differentiable function defined in (-1,1). If f(0)=2 and [itex]f'(x)=f(x)+e^x(\sqrt{x^4+1})[/itex] , then find [itex]\frac{df^{-1}(x)}{dx}[/itex] at x=2.

    2. Relevant equations

    3. The attempt at a solution
    [itex]\frac{dy}{dx}=y+e^x \sqrt{x^4+1} \\
    dy=(y+e^x \sqrt{x^4+1})dx[/itex]

    Integrating both sides
    [itex]y=xy+\int (e^x\sqrt{x^4+1})dx[/itex]

    I don't know the integration ahead.
     
  2. jcsd
  3. May 27, 2013 #2

    Curious3141

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    Homework Helper

    You can't separate variables like that. Your solution of the d.e. is wrong.

    But in any case, you don't need to solve that d.e. Do you know how to find the derivative of an inverse function at a given point without actually finding the inverse explicitly?

    You might want to take a look at an earlier post of mine: https://www.physicsforums.com/showpost.php?p=4296589&postcount=9
     
  4. May 27, 2013 #3

    utkarshakash

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    OK. I followed your method and got the answer as 1/3. Is this correct?
     
  5. May 28, 2013 #4

    Curious3141

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    Correct.
     
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