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Chain Rule

  1. Dec 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Find g'(x)

    2. Relevant equations
    Answer stated as:
    a'(x)=(18-x^2)^1/2 - x^2/(18-x^2)^1/2

    3. The attempt at a solution

    Having trouble with this solution. The chain rule states that f(x)g(x) = f'(x)g(x)+g'(x)f(x) so the first term in the solution is obviously (18-x^2)^1/2.

    Where I run into problems is the second term with the numerator being x^2 when I thought it should only be x. Simplifying the problem into f(x)=(18-x^2)^1/2 the chain rule states it the derivative should be 1/2(18-x^2)(0-2x)=-x/(18-x^2)^1/2. Am I wrong or is the stated solution wrong?
  2. jcsd
  3. Dec 14, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You forgot about f(x) = x, which gives you the second x.
  4. Dec 14, 2008 #3
    Ugh, that is so... dirty. Thanks, that was pretty simple.
  5. Dec 14, 2008 #4


    Staff: Mentor

    That's not the chain rule; it's the product rule. The chain rule is used to find the derivative of a composite function, f(g(x)).
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