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Basic Derivative

  1. Feb 6, 2006 #1
    Ok, so I jsut entered Calculus and I'm currently stuck on a problem (no laughing).

    Find the derivative of the algebraic function:

    [tex] x^2\sqrt{9-x^2} [/tex]

    I tried using the chain rule, but I get confused when composing because x exists in 2 places when you plug in g(x) back into f`(x)
    Last edited by a moderator: Feb 6, 2006
  2. jcsd
  3. Feb 6, 2006 #2


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    The thing to learn is that all of the derivative rules are applied just as you would apply ordinary arithmetic rules.

    For example, for the function [itex]f(x) = x^2 \sqrt{9 - x^2}[/itex], how would you go about computing f(1.5)?

    The first thing you would probably do is to compute (1.5)², right?

    So, the first thing you should do when computing the derivative is to find the derivative of x².

    Could you show what you have done on the problem? (preferably what you have done after trying to use my hint)
    Last edited: Feb 6, 2006
  4. Feb 6, 2006 #3
    I got a bit further. Derivative [tex] x^2 [/tex] is [tex] 2x [/tex]. First, I used the quotient rule and set [tex]f(x)[/tex] to [tex]x^2[/tex] and [tex]g(x)[/tex] to [tex]\sqrt{9 - x^2}[/tex] then used the chain rule to find the derivative of g(x)
  5. Feb 6, 2006 #4
    The quotient rule really won't help here since you don't have a quotient, but you do have a product...
  6. Feb 6, 2006 #5
    Err, product rule rather, sorry.
  7. Feb 6, 2006 #6


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    Ok, so show us how you tried to do the chain rule, and what the problem is!

    (You said something about there being multiple x's, but there is only one x in your g(x))
  8. Feb 6, 2006 #7
    Never mind, got it. Was quite a bit of work. Thanks to you both.
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