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Math Help - Finding derivatives using the product rule

  1. #1
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    Finding derivatives using the product rule

    I'm having trouble getting the correct answer when using the product rule to find a derivative.

    For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
    I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)

    however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

    how do I get the answer in this form???

    thanks to everyone in advance
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  2. #2
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    Re: Finding derivatives using the product rule

    Quote Originally Posted by JellyOnion View Post
    I'm having trouble getting the correct answer when using the product rule to find a derivative.

    For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
    I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)

    however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

    how do I get the answer in this form???

    thanks to everyone in advance
    Let's see:

    you would actually use product rule with chain rule(for this (3x+1)^(3/2)), so we will have -

    f'(x) = ((3x+1)^(3/2))' * (2x+4) + ((3x+1)^(3/2))*(2x+4)' =

    (3/2)*(3x+1)^(1/2) *(3)*(2x+4) + ((3x+1)^(3/2))*(2x) =

    3(3x+1)^(1/2) *(2x+4) + ((3x+1)^(3/2))*(2x) =...

    would you need any help further to factorize or you are ok?
    Thanks from JellyOnion
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  3. #3
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    Re: Finding derivatives using the product rule

    Quote Originally Posted by JellyOnion View Post
    I'm having trouble getting the correct answer when using the product rule to find a derivative.

    For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
    ]
    So this is of the form f(x)g(x) with f(x)= (3x+ 1)^(3/2) and g(x)= 2x+ 4.
    Of course, the product rule says (fg)'= f'g+ fg'
    With f(x)= (3x+ 1)^{3/2}, f'(x)= (3/2)(3x+1)^(1/2)(3)= (9/2)(3x+1)^{1/2} and with g(x)= 2x+ 4, g'(x)= 2.
    f'g= (9/2)(3x+1)^{1/2}(2x+ 4) and fg'= 2(3x+1)^{3/2}
    [quote]I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)[quote]
    You appear to be thinking that (9/2)(3x+ 1)^(1/2)(2x+ 4)= (9/2)[3x^{1/2}+ 4](2x+4) and that 2(3x+1)^{3/2}= 2(3x^{1/2}+ 1).
    That is NOT true. In particular, (3x+1)^{3/2} is NOT 3x^(3/2)+ 1.

    however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

    how do I get the answer in this form???

    thanks to everyone in advance
    Thanks from JellyOnion
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    Re: Finding derivatives using the product rule

    Thank you dokrbb very much for your help but I'm still a little confused how you would factorize that to the answer.
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  5. #5
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    Re: Finding derivatives using the product rule

    Ohhh thanks hallsoivy i see, very much appreciate the help
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