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Math Help - please explain to me this exercise about the chain rule

  1. #1
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    please explain to me this exercise about the chain rule

    Hello. In a few hours I have to take a test concerning derivatives, I understand almost everything, however I'm having a hard time trying to understand an exercise which is already solved in the book, this is the excercise

    find f'(x) if f(x) = (2x^2+3)^4 (3x-1)^5

    and so they solve the excercise, they apply product rule followed by the general power rule, but I'm so confused, I'm lost, I don't get it, i don't understand how they solve that excercise.

    Could you please explain to me how to solve an exercise of that nature? please, with easy steps.
    thank you.
    Last edited by jhonwashington; October 21st 2008 at 11:36 PM. Reason: missed a word
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  2. #2
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    If you let  (2x^2+3)^4  = A and  (3x-1)^5 = B
    You can see that the product rule will yield the derivative:  \frac{dA}{dx}B + \frac{dB}{dx}A

    With this in hand, you must find the derivatives of A and B.

    To do this you can use the chain rule:  \frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}

    For the example of A, let  2x^2+3 = u

    You can combine all of this into one formula, but it's easiest done in seperate steps.
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