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Math Help - Using the chain rule

  1. #1
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    Using the chain rule

    I just want to check another answer to see I am on the right track. I do not think I done this one correctly.

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  2. #2
    Senior Member Pinkk's Avatar
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    Totally wrong I'm afraid (I have no idea what you did). This requires the product rule and the chain rule.

    Let f(x)=x^{2},g(x)=(x-2)^{4},h(x)=f(x)g(x)

    The product rule: h'(x)=f(x)g'(x)+f'(x)g(x)

    Applying the chain rule here:

    h'(x)=x^{2}(\frac{d}{dx}(x-2)^{4})+(\frac{d}{dx}x^{2})(x-2)^{4}

    You will need to apply the chain rule to (x-2)^{4}, which ends up being 4(x-2)^{3}(\frac{d}{dx}(x-2)) which is simply 4(x-2)^{3}. Getting back to the whole derivative we will have:

    h'(x)=4x^{2}(x-2)^{3}+2x(x-2)^{4}
    Last edited by Pinkk; March 23rd 2009 at 04:00 PM.
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  3. #3
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    So, how did you determine that you had to use the product rule?

    My book states nothing about learning to use the product rule to solve this problem?

    I am very confused?
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  4. #4
    Senior Member Pinkk's Avatar
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    You have a function such that h(x)=f(x)g(x), where f(x)=x^{2} and g(x)=(x-2)^{4}. If you have not learned the product rule yet, then your only other option is to expand (x-2)^{4} and multiply every term by x^{2}, and then differentiate.
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