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Differentiation from first principles

  1. Oct 29, 2011 #1

    Electrifying

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    Hey guys, I've got the following 2 mark question on a problem sheet, but I can't seem able to do it. I'd appreciate any help, thanks.

    Differentiate, from first principles, the following:

    [tex]y=\sqrt(a^2-x^2)[/tex]

    I know I have to take the limit as δx tends to 0 of [(f(x+δx)- f(x)]/δx but can't seem to manipulate the resultant expression in any way to get closer to an answer. I have never used this Latex thingy before, so hopefully it comes out OK.

    Thanks in advance!
     
    Last edited: Oct 29, 2011
    Electrifying, Oct 29, 2011
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  3. Oct 29, 2011 #2

    Mark44

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    There is no x in the formula for your function. Are a and b constants or are they variables? If a and b are constants, then the graph of your function is a horizontal line, making the derivative zero.
     
    Mark44, Oct 29, 2011
  4. Oct 29, 2011 #3

    Electrifying

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    Sorry, just a typo, [tex]b^2[/tex] should be [tex]x^2[/tex].

    But a is just a constant yes.
     
    Electrifying, Oct 29, 2011
  5. Oct 29, 2011 #4

    ehild

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    As for Latex thingies, use curly brackets{} for the argument of the square root.

    [tex]y=\sqrt{a^2-x^2}[/tex]

    It is a good method to eliminate difference of square roots by multiplying and dividing with the sum of the same square roots.
    Write up the the expression (f(x+δx)-f(x))/δx with the square roots and you will see what I mean.


    ehild
     
    ehild, Oct 29, 2011
  6. Oct 30, 2011 #5

    Electrifying

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    Thank you very much for that, my final answer of

    [tex]\frac{dy}{dx} =-\frac{x}{\sqrt{a^2-x^2}}[/tex]

    Agrees with the answer obtained if you just differentiate 'normally'. Thanks again!
     
    Electrifying, Oct 30, 2011
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