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Derivative of f(x)=(1-x)2(1+x)3?

  1. Mar 3, 2010 #1
    what is the first derivative of f(x)=(1-x)2(1+x)3?
     
  2. jcsd
  3. Mar 3, 2010 #2

    radou

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    Re: Derivatives

    You have to apply two rules here - the rule for taking the derivative of a product of functions, and the rule for taking the derivative of a composition of functions. What is the product, and what is the composition? What are the composition and product rules?
     
  4. Mar 3, 2010 #3
    Re: Derivatives

    you see, that's the reason why I posted this thread. I'm somehow confused on what to use. Will I use the power rule or the product rule?? if i'm gonna use the power rule, i'll arrive on an answer like this: 2(1-x)*3(1+x)2

    is that correct??
     
  5. Mar 3, 2010 #4

    radou

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    Re: Derivatives

    You have to use both.

    Let's say f (x) = g(x) * h(x), so g(x) = (1-x)^2 and h(x) = (1+x)^3.

    First, apply the product rule, since you have a product of functions, i.e. f'(x) = g'(x)*h(x) + g(x)*h'(x).

    Now you only need to apply the composition rule to sind g'(x) and h'(x).
     
  6. Mar 3, 2010 #5
    Re: Derivatives

    No, because you need to apply the product rule.

    (fg)' is not f'g'!!

    The rule is:

    (fg)'=f'g+fg'.

    Only when you apply this rule, you can take the derivative of f and g by the power rule when needed.
     
  7. Mar 3, 2010 #6
    Re: Derivatives

    alright2x...got it...now i'm enlightened..thanks a lot for the help.. :)
     
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