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Chain Rule Derivative

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Differentiate [tex] f(x)=(3x^{2}+4)^{3}(5-3x)^{4}[/tex]



    2. Relevant equations
    N/A



    3. The attempt at a solution
    I can see that this derivative is a product, yet also involves using chain rule. With this being said, am i just supposed to evaluate these separately using chain rule for each then multiply the results together? Or is there another way to differentiate this? Thanks in advance.
     
  2. jcsd
  3. Oct 11, 2009 #2

    Pengwuino

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    Gold Member

    Take it as [tex]f(x) = g(u(x))h(v(x))[/tex]. Then [tex]f'(x) = g'(u)h(v) + h'(v)g(u)[/tex] where for example [tex] g'(u) = \frac{dg(u)}{dx} = \frac{dg(u)}{du}*\frac{du}{dx}[/tex], your standard chain rule.
     
  4. Oct 11, 2009 #3
    Ah yes I see it now, thank you very much!
     
  5. Oct 11, 2009 #4
    This is a product rule question, however, to take the derivative of this, you'll need the derivative of first and the derivative of the 2nd, thus the chain rule.

    If you don't want to use the chain rule, you can expand both and use the product rule. :)
     
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