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Derivative of inverse secant

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of sec[itex]^{-1}[/itex]([itex]\frac{\sqrt{1+x^{2}}}{x}[/itex])

    2. Relevant equations

    sec[itex]^{-1}[/itex]=[itex]\frac{U'}{U\sqrt{U^{2}-1}}[/itex]


    3. The attempt at a solution

    U'=-[itex]\frac{1}{x^{2}\sqrt{1+x^{2}}}[/itex]



    U[itex]\sqrt{U^{2}-1}[/itex]= [itex]\frac{\sqrt{1+x^{2}}}{x^{2}}[/itex]


    Therefore the derivative is -[itex]\frac{1}{1+x^{2}}[/itex]


    I'm starring to feel more confident with these derivatives and if this is correct, I think I will have come ever closer to mastering this skill. Can someone tell me if this is correct (the answer isn't in my text)?

    p.s. I know that the first "U" in the denominator of the relevant equation should be in absolute value brackets but I couldn't find them in the menu.

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
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  2. jcsd
  3. Mar 10, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your answer is right.
     
  4. Mar 10, 2012 #3
    Thank you
     
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