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Derivatives of square roots

  1. Apr 13, 2004 #1
    How can i find the derivative of a function like this:
    f(x) = sqrt( 1 - x² )
     
  2. jcsd
  3. Apr 13, 2004 #2

    Hurkyl

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    Do you know how to write a square root with exponents?
     
  4. Apr 13, 2004 #3
    (1 - x² )^(1/2) ?
     
  5. Apr 13, 2004 #4

    Hurkyl

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    That's right! Now, you just need to apply what you know about differentiating expressions like that.
     
  6. Apr 13, 2004 #5
    si will that be:
    1/2((1-x²)/2)^(-1/2)

    ?
     
  7. Apr 13, 2004 #6

    HallsofIvy

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    Not quite. You have one too many "1/2"s (you don't want that "/2" inside the square root and you didn't use the chain rule.

    You need to multiply by the derivative of 1-x2.
     
    Last edited: Jul 17, 2009
  8. May 13, 2009 #7
    Hi,

    I have a similar problem, I need to differentiate sqrt(x^2 + y^2) in terms of x and y.
    Starting this I took the simple step (x^2 + y^2)^(1/2)...

    My next step is a guess and I am lost after it....(1/2)(x^2 + y^2)(-1/2)....

    Any help would be much appreciated.
     
  9. May 13, 2009 #8

    jbunniii

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    If by "in terms of x and y", you mean you want to calculate the partial derivatives, then for the partial derivative with respect to x, treat y as a constant and differentiate with respect to x as you normally would a function of one variable. For the partial derivative with respect to y, treat x as constant.
     
  10. May 13, 2009 #9
    thanks, would I do this by...

    df/dx = 1/2(x^2 + y^2)^(-1/2).2x = x/sqrt(x^2 + y^2) and...

    df/dy = 1/2(x^2 + y^2)^(-1/2).2y = y/sqrt(x^2 + y^2) ?

    thanks for your help so quickly.
     
  11. May 13, 2009 #10

    jbunniii

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    Looks good to me.
     
  12. Jul 16, 2009 #11
    What if i have a problem similar to these however now its 4/ ^5sqrt(x^5)
     
  13. Jul 17, 2009 #12
    If that is meant to be 4^(5(sqrt(x^5))), then you can easily rewrite this to equal
    4^(5(x^(5/2)) And using what you know from differentiating exponentials and chain rule, you should be able to get the rest.
     
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